Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sec ^{2} x}{\sqrt{16+\tan ^{2} x}} d x=?$ A. $\log \left|\tan x+\sqrt{\tan ^{2} x+16}\right|+C$ B. $\log \left|x+\sqrt{\tan ^{2} x+16}\right|+C$ C. $\log \left|\tan x-\sqrt{\tan ^{2} x+16}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x^{2} d x}{\sqrt{x^{6}+a^{6}}} d x=?$ A. $\frac{1}{3} \log \left|x^{6}+a^{6}\right|+C$ B. $\frac{1}{3} \tan ^{-1}\left(\frac{x^{3}}{a^{3}}\right)+C$ C. $\frac{1}{3} \log \left|x^{3}+\sqrt{x^{6}+a^{6}}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{x^{2}-6 x+10}}=?$ A. $\log \left|x+\sqrt{x^{2}-6 x+10}\right|+C$ B. $\log \left|(x-3)+\sqrt{x^{2}-6 x+10}\right|+C$ C. $\log \left|x-\sqrt{x^{2}-6 x+10}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: A. $\log \left|(x-3)+\sqrt{x^{2}-6 x+8}\right|+C$ B. $\log \left|x+\sqrt{x^{2}-6 x+8}\right|+C$ C. $\log \left|(x-3)-\sqrt{x^{2}-6 x+8}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{x^{2}+6 x+5}}=?$ A. $\log \left|x+\sqrt{x^{2}+6 x+5}\right|+C$ B. $\log \left|x-\sqrt{x^{2}+6 x+5}\right|+C$ C. $\log \left|(x+3)+\sqrt{x^{2}+6 x+5}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{2-4 x+x^{2}}}=?$ A. $\log \left|(x-2)+\sqrt{x^{2}-4 x+2}\right|+C$ B. $\log \left|x+\sqrt{x^{2}-4 x+2}\right|+C$ C. $\log \left|x-\sqrt{x^{2}-4 x+2}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cos x}{\sqrt{\sin ^{2} x-2 \sin x-3}} d x=?$ A. $\log \left|\sin x+\sqrt{\sin ^{2} x-2 \sin x-3}\right|+C$ B. $\log \left|(\sin x-1)+\sqrt{\sin ^{2} x-2 \sin x-3}\right|+C$ C. $\log \left|(\sin x-1)-\sqrt{\sin ^{2} x-2 \sin x-3}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{x^{2}-3 x+2}}=?$ A. $\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^{2}-3 x+2}\right|+C$ B. $\log \left|x+\sqrt{x^{2}-3 x+2}\right|+C$ C. $\log \left|x-\sqrt{x^{2}-3 x+2}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(1-\mathrm{e}^{2 \mathrm{x}}\right)}=?$ A. $\log \left|e^{x}+\sqrt{e^{2 x}-1}\right|+C$ B. $\log \left|e^{-x}+\sqrt{e^{-2 x}-1}\right|+C$ C. $-\log \left|e^{-x}+\sqrt{e^{-2 x}-1}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sec ^{2} x}{\sqrt{\tan ^{2} x-4}} d x=?$ A. $\log \left|\tan x-\sqrt{\tan ^{2} x-4}\right|+C$ B. $\log \left|\tan x+\sqrt{\tan ^{2} x-4}\right|+C$ C. $\frac{1}{2} \log \left|\tan x+\sqrt{\tan ^{2} x-4}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sin x}{\sqrt{4 \cos ^{2} x-1}}=?$ A. $-\frac{1}{2} \log \left|2 \cos x+\sqrt{4 \cos ^{2} x-1}\right|+C$ B. $-\frac{1}{3} \log \left|2 \cos x+\sqrt{4 \cos ^{2} x-1}\right|+C$ C. $-\frac{1}{6} \log \left|2 \cos x+\sqrt{2 \cos ^{2} x-1}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x^{2}}{x^{6}-1} d x=?$ A. $\frac{1}{2} \log \left|\mathrm{x}^{3}+\sqrt{\mathrm{x}^{6}-1}\right|+\mathrm{C}$ B. $\frac{1}{3} \log \left|x^{3}+\sqrt{x^{6}-1}\right|+C$ C. $\frac{1}{3} \log \left|\mathrm{x}^{3}-\sqrt{\mathrm{x}^{6}-1}\right|+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{4 x^{2}-9}}=?$ A. $\frac{1}{2} \log \left|2 x+\sqrt{4 x^{2}-9}\right|+C$ B. $\frac{1}{4} \log \left|x+\sqrt{4 x^{2}-9}\right|+C$ C. $\log \left|2 x+\sqrt{4 x^{2}-9}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{\mathrm{x}^{2}-16}}=?$ A. $\sin ^{-1}\left(\frac{x}{4}\right)+C$ B. $\log \left|x+\sqrt{x^{2}-16}\right|+C$ C. $\log \left|x-\sqrt{x^{2}-16}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{1+2 \mathrm{x}-3 \mathrm{x}^{2}}}=?$ A. $\frac{1}{\sqrt{3}} \sin ^{-1}\left(\frac{3 x-1}{2}\right)+C$ B. $\frac{1}{\sqrt{2}} \sin ^{-1}\left(\frac{2 x-1}{3}\right)+C$ C. $\frac{1}{\sqrt{3}} \sin ^{-1}\left(\frac{2 \mathrm{x}-1}{3}\right)+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{x-x^{2}}}=?$. A. $\sin ^{-1}(x-1)+C$ B. $\sin ^{-1}(x+1)+C$ C. $\sin ^{-1}(2 x-1)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{16-6 x-x^{2}}}=?$ A. $\sin ^{-1}\left(\frac{x-3}{5}\right)+C$ B. $\sin ^{-1}\left(\frac{\mathrm{x}+3}{5}\right)+\mathrm{C}$ C. $\frac{1}{5} \sin ^{-1}(x+3)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{2+2 x-x^{2}}}=?$ A. $\sin ^{-1}\left(\frac{x-1}{\sqrt{3}}\right)+C$ B. $\sin ^{-1}\left(\frac{x-1}{\sqrt{2}}\right)+C$ C. $\sin ^{-1} \sqrt{3}(x-1)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{3 x^{2}}{\sqrt{9-16 x^{6}}} d x=?$ A. $\frac{1}{4} \sin ^{-1}\left(\frac{x^{3}}{3}\right)+C$ B. $\frac{1}{4} \sin ^{-1}\left(\frac{4 x^{3}}{3}\right)+C$ C. $4 \sin ^{-1}\left(\frac{x^{3}}{4}\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{x(1-2 x)}=?$ A. $\frac{1}{\sqrt{2}} \sin ^{-1}(2 x-1)+C$ B. $\frac{1}{\sqrt{2}} \sin ^{-1}(2 x+1)+C$ C. $\frac{1}{\sqrt{2}} \sin ^{-1}(4 x+1)+C$ D. $\frac{1}{\sqrt{2}} \sin ^{-1}(4 x-1)+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{x}-\mathrm{x}^{2}}}=?$ A. $\sin ^{-1}(x+1)+C$ B. $\sin ^{-1}(x-2)+C$ C. $\sin ^{-1}(x-1)+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=?$ A. $\sin ^{-1}\left(2^{x}\right) \log 2+C$ B. $\frac{\sin ^{-1}\left(2^{x}\right)}{\log 2}+C$ C. $\sin ^{-1}\left(2^{x}\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\cos x}{\sqrt{4-\sin ^{2} x}}=?$ A. $\sin ^{-1} \frac{x}{2}+C$ B. $\sin ^{-1}\left(\frac{1}{2} \cos x\right)+C$ C. $\sin ^{-1}(2 \sin x)+C$ D. $\sin ^{-1}\left(\frac{1}{2} \sin x\right)+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{16-4 x^{2}}}=?$ A. $\frac{1}{2} \sin ^{-1} \frac{x}{2}+C$ B. $\frac{1}{4} \sin ^{-1} \frac{x}{2}+C$ C. $\frac{1}{2} \sin ^{-1} \frac{x}{4}+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{4-9 x^{2}}}=?$ A. $\frac{1}{3} \sin ^{-1} \frac{x}{3}+C$ B. $\frac{2}{3} \sin ^{-1}\left(\frac{2 x}{3}\right)+C$ C. $\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)+C$ D. none of these Solution:...
Read More →