Question

Write a value of

\[\int \tan^3 x \sec^2 x \text{ dx }\].

 

Answer 1

Let I=\[\int\]  tan³ x . sec² x dx

Let tan x = t
⇒ sec²x dx = dt

\[\therefore\]\[\int\] t³ . dt

\[= \frac{t^4}{4} + C\]
\[ = \frac{\tan^4 x}{4} + C \left( \because t = \tan x \right)\]