What is the integral of tan^2(sqrt(x)) ?

The integral of tan^2(sqrt(x)) is -x+2(sqrt(x)tan(sqrt(x))+ln|cos(sqrt(x))|)+C

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integral of tan^2(sqrt(x))

\int tan^{2} (x) d x

- x + 2 (x tan (x) + ln cos (x)) + C

Solution steps

\int tan^{2} (x) d x

Rewrite using trig identities

= \int - 1 + sec^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d x + \int sec^{2} (x) d x

\int 1 d x = x

\int sec^{2} (x) d x = 2 (x tan (x) + ln cos (x))

= - x + 2 (x tan (x) + ln cos (x))

Add a constant to the solution

= - x + 2 (x tan (x) + ln cos (x)) + C

What is the integral of tan^2(sqrt(x)) ?
The integral of tan^2(sqrt(x)) is -x+2(sqrt(x)tan(sqrt(x))+ln|cos(sqrt(x))|)+C