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)

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

- sec (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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