What is the integral of (sec^2(x))/(tan(x)+1) ?

The integral of (sec^2(x))/(tan(x)+1) is ln|tan(x)+1|+C

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integral of (sec^2(x))/(tan(x)+1)

\int \frac{sec ^{2} ( x )}{tan ( x ) + 1} d x

ln ∣ tan (x) + 1 ∣ + C

Solution steps

\int \frac{sec ^{2} ( x )}{tan ( x ) + 1} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = tan (x) + 1

= ln ∣ tan (x) + 1 ∣

Add a constant to the solution

= ln ∣ tan (x) + 1 ∣ + C

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What is the integral of (sec^2(x))/(tan(x)+1) ?
The integral of (sec^2(x))/(tan(x)+1) is ln|tan(x)+1|+C