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

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

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integral of (sin(tan(x)))/(cos^2(x))

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

- cos (tan (x)) + C

Solution steps

\int \frac{sin ( tan ( x ) )}{cos ^{2} ( 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

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\int \frac{8}{9} csc^{2} (\frac{x}{9}) d x

\int (12 x^{2} + 6 x - 5) d x

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