Solve this following
Question: Evaluate the following integrals: $\int \cos ^{4} x \sin ^{3} x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos ^{3} x \sin ^{4} x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sec ^{4} x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin ^{3} x \cos x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos 2 x \cos 4 x \cos 6 x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos ^{4} x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin x \sqrt{1+\cos 2 x} d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin 6 x \cos x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin 4 x \sin 8 x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos 4 x \cos 3 x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin 3 x \cos 4 x d x$ Solution:...
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Question: Evaluate the following integrals:. (i) $\int \frac{1-\cos x}{1+\cos x} d x$ (ii) $\int \frac{1+\cos x}{1-\cos x} d x$ Solution:...
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Question: Evaluate the following integrals: (i) $\left(\frac{1-\cos 2 x}{1+\cos 2 x}\right) d x$ (ii) $\left(\frac{1+\cos 2 \mathrm{x}}{1-\cos 2 \mathrm{x}}\right) \mathrm{dx}$ Solution:...
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Question: Evaluate the following integrals: $\int \sin ^{7}(3-2 x) d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos ^{3}(3 x+5) d x$ Solution:...
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Question: Evaluate the following integrals: (i) $\int \sin ^{2} n x d x$ (ii) $\int \sin ^{5} \mathrm{x} d \mathrm{x}$ Solution:...
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Question: Evaluate the following integrals: (i) $\int \cos ^{2}(x / 2) d x$ (ii) $\int \cot ^{2}(\mathrm{x} / 2) \mathrm{dx}$ Solution:...
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Question: Evaluate the following integrals: (i) $\int \sin ^{2} x d x$ (ii) $\int \cos ^{2} \mathrm{xdx}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\sqrt{\sin ^{3} x \cos x}}=?$ A. $2 \sqrt{\tan x}+C$ B. $2 \sqrt{\cot x}+C$ C. $-2 \sqrt{\tan x}+C$ D. $\frac{-2}{\sqrt{\tan x}}+C$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sqrt{e^{x}-1} d x=?$ A. $\frac{2}{3}\left(e^{x}-1\right)^{3 / 2}+C$ B. $\frac{1}{2} \cdot \frac{\mathrm{e}^{\mathrm{x}}}{\sqrt{\mathrm{e}^{\mathrm{x}}-1}}+\mathrm{C}$ e C. $2 \sqrt{e^{x}-1}-2 \tan ^{-1} \sqrt{e^{x}-1}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(\cos +\sin x)}{(1-\sin 2 x)} d x=?$ A. $\log |\sin x-\cos x|+C$ B. $\frac{1}{(\cos x-\sin x)}+C$ C. $\log |\cos x+\sin x|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sqrt{\tan x}}{\sin x+\cos x} d x=?$ A. $2 \sqrt{\tan x}+C$ B. $2 \sqrt{\cot x}+C$ C. $2 \sqrt{\sec x}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin ^{3}(2 x+1) d x=?$ A. $\frac{1}{8} \sin ^{4}(2 x+1)+C$ B. $\frac{1}{2} \cos (2 x+1)+\frac{1}{3} \cos ^{3}(2 x+1)+C$ C. $-\frac{1}{2} \cos (2 x+1)+\frac{1}{6} \cos ^{3}(2 x+1)+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\log \tan x}{\sin x \cos x} d x=?$ A. $\log \{\log (\tan x) \mid+C$ B. $\frac{1}{2}(\log \tan x)^{2}+C$ C. $\log (\sin x \cos x)+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sec ^{4} x \tan x d x=?$ A. $\frac{1}{2} \sec ^{2} x+\frac{1}{4} \sec ^{4} x+C$ B. $\frac{1}{2} \tan ^{2} \mathrm{x}+\frac{1}{4} \tan ^{4} \mathrm{x}+\mathrm{C}$ C. $\frac{1}{2} \sec x+\log |\sec x+\tan x|+C$ D. none of these Solution:...
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