What is the Integral of ${sec}^{2} (x) \cdot {tan}^{2} (x)$ $sec^2(x) * tan^2(x)$ ?

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Answer 1 · 2018-06-07T10:31:30

$\frac{1}{3} {tan}^{3} x + C$ $1/3tan^3x+C$ .

Suppose that, $I = \int {sec}^{2} x {tan}^{2} x d x$ $I=intsec^2xtan^2xdx$ .

If we subst. $tan x = y, then, {sec}^{2} x d x = d y$ $tanx=y," then, "sec^2xdx=dy$ .

$:. I=inty^2dy=y^3/3=1/3tan^3x+C$ .

What is the Integral of sec^2(x) * tan^2(x)sec2(x)⋅tan2(x)sec^2(x) * tan^2(x)?