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

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

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

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

- cos (tan (x)) + C

Solution steps

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

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = tan (x)

= - cos (tan (x))

Add a constant to the solution

= - cos (tan (x)) + C

\int \frac{3 x ^{2}}{sec ( 2 x )} d x

\int e^{2 x - y} d x

\int x^{2} + 15 d x

9 - x^{2}

\int \frac{2}{3 x ^{4}} d x

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