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

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

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

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

sin (x) + C

Solution steps

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

Simplify

\frac{1}{1 + tan ^{2} ( x )} : cos^{2} (x)

= \int cos^{2} (x) d x

cos^{2} (x) = (cos (x)),

assuming

cos (x) \geq 0

= \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= sin (x)

Add a constant to the solution

= sin (x) + C

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