What is the integral of (sin(4x))/(cos^2(4x)) ?

The integral of (sin(4x))/(cos^2(4x)) is 1/4 sec(4x)+C

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integral of (sin(4x))/(cos^2(4x))

\int \frac{sin ( 4 x )}{cos ^{2} ( 4 x )} d x

\frac{1}{4} sec (4 x) + C

Solution steps

\int \frac{sin ( 4 x )}{cos ^{2} ( 4 x )} d x

Rewrite using trig identities

= \int sec (4 x) tan (4 x) d x

Apply u-substitution

: \int \frac{1}{4} d u

= \int \frac{1}{4} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{4} u

Substitute back

u = sec (4 x)

= \frac{1}{4} sec (4 x)

Add a constant to the solution

= \frac{1}{4} sec (4 x) + C

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What is the integral of (sin(4x))/(cos^2(4x)) ?
The integral of (sin(4x))/(cos^2(4x)) is 1/4 sec(4x)+C