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Question

Evaluate $$\displaystyle \int\frac{\sin^{10}x}{\cos^{12}x}dx$$


A
tan11x11+c
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B
tan10x10+c
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C
10tan9x+c
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D
tan9x10+c
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Solution

The correct option is A $$\displaystyle \frac{\tan^{11}x}{11}+c $$
$$\displaystyle \int \ \dfrac{\sin ^{10}x}{\cos ^{12}x}\ dx$$
$$\displaystyle \int \ \tan ^{10}x.\ \sec ^{2}x.\ dx$$
We know that $$\sec ^{2}x.\ dx.=d(\tan x)$$
$$\displaystyle \int \ \tan ^{10}x\ d(\tan x)$$
$$=\ \dfrac{\tan ^{11}x}{11}+c$$
$$\displaystyle \int \ \dfrac{\sin ^{10}x}{\cos ^{12}x}\ dx=\ \dfrac{\tan ^{11}x}{11}+c$$

Mathematics

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