What is the integral of (sec^2(arctan(2x)))/(1+4x^2) ?

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

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integral of (sec^2(arctan(2x)))/(1+4x^2)

\int \frac{sec ^{2} ( arctan ( 2 x ) )}{1 + 4 x ^{2}} d x

x + C

Solution steps

\int \frac{sec ^{2} ( arctan ( 2 x ) )}{1 + 4 x ^{2}} d x

\frac{sec ^{2} ( arctan ( 2 x ) )}{1 + 4 x ^{2}} = 1

= \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

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