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

The integral of (sec^2(w))/(1+tan^2(w)) is w+C

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

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

w + C

Solution steps

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

Rewrite using trig identities

= \int 1 d w

Integral of a constant:

\int a d x = a x

= 1 \cdot w

Simplify

= w

Add a constant to the solution

= w + C

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