How do you integrate $\int {tan}^{3} x {sec}^{2} x$ $int tan^3xsec^2x$ using substitution?

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Answer 1 · 2018-03-14T07:45:23

Use the substitution $u = tan x$ $u=tanx$ .

Let

$I = \int {tan}^{3} x {sec}^{2} d x$ $I=inttan^3xsec^2dx$

Apply the substitution $u = tan x$ $u=tanx$ :

$I = \int u^{3} d u$ $I=intu^3du$

Integrate directly:

$I = \frac{1}{4} u^{4} + C$ $I=1/4u^4+C$

Reverse the substitution:

$I = \frac{1}{4} {tan}^{4} x + C$ $I=1/4tan^4x+C$

How do you integrate int tan^3xsec^2x∫tan3xsec2xint tan^3xsec^2x using substitution?