Mathematics

Evaluate the following integrals:$\displaystyle \int { \tan ^{ 3 }{ x } \sec ^{ 2 }{ x } } dx$

SOLUTION
$\displaystyle\int{{\tan}^{3}{x}{\sec}^{2}{x}dx}$

Let $t=\tan{x}\Rightarrow\,dt={\sec}^{2}{x}dx$

$=\displaystyle\int{{t}^{3}\,dt}$

We know that $\displaystyle\int{{x}^{n}dx}=\dfrac{{x}^{n+1}}{n+1}+c$

$=\dfrac{{t}^{4}}{4}+c$

$=\dfrac{{\tan}^{4}{x}}{4}+c$ where $t=\tan{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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