Mathematics

 Find Integrals of given function: $$\int_{}^{} {\tan \theta } {\tan ^2}\theta {\sec ^2}\theta d\theta $$


ANSWER

$$\dfrac{\tan^4\theta}{4}+c$$


SOLUTION
$$\int_{}^{} {\tan \theta } {\tan ^2}\theta {\sec ^2}\theta d\theta=\int\tan^3\theta\sec^2\theta d\theta$$

Let $$t=\tan\theta\\dt=\sec^2\theta d\theta$$

Hence,
$$\int t^3dt=\dfrac{t^4}{4}+c=\dfrac{\tan^4\theta}{4}+c$$
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Single Correct Medium Published on 17th 09, 2020
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