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

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

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

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

x + C

Solution steps

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

Rewrite using trig identities

= \int 1 d x

Integral of a constant:

\int a d x = a x

= 1 \cdot x

Simplify

= x

Add a constant to the solution

= x + C

\frac{d}{d x} (arctan (x) + 2 x - 2)

y = x^{\frac{15}{16}}

\int 2 x - \frac{1}{2 x} d x

\int \frac{1}{y + 1} d y

\int sin^{3} (4 x) cos^{9} (4 x) d x

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