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

The integral of (sin(v))/(cos^2(v)) is sec(v)+C

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integral of (sin(v))/(cos^2(v))

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

sec (v) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = cos (v)

= - (- \frac{1}{cos ( v )})

Simplify

- (- \frac{1}{cos ( v )}) : sec (v)

= sec (v)

Add a constant to the solution

= sec (v) + C

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What is the integral of (sin(v))/(cos^2(v)) ?
The integral of (sin(v))/(cos^2(v)) is sec(v)+C