What is the integral of sin(x)sec^2(x) ?

The integral of sin(x)sec^2(x) is sec(x)+C

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integral of sin(x)sec^2(x)

integral

sin (x) sec^{2} (x)

sec (x) + C

Solution steps

\int sin (x) sec^{2} (x) d x

Rewrite using trig identities

= \int sin (x) (1 + tan^{2} (x)) d x

Apply Integration By Parts

= - sec (x) - \int - 2 sec (x) tan (x) d x

\int - 2 sec (x) tan (x) d x = - 2 sec (x)

= - sec (x) - (- 2 sec (x))

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

What is the integral of sin(x)sec^2(x) ?
The integral of sin(x)sec^2(x) is sec(x)+C