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

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

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

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

x + C

Solution steps

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

\int (x + 1) (x + 1) d x

\int \frac{x ^{2} - 4}{x ^{3} - 12 x + 7} d x

\int \frac{3 ^{x}}{4 + 3 ^{2 x}} d x

\int sec (\frac{x + 2}{3}) d x

\int (x^{2} + 3 x + 2) e^{2 x} d x

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