What is the integral of 1/(cos^2(x)+sin^2(x)) ?

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

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integral of 1/(cos^2(x)+sin^2(x))

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

x + C

Solution steps

\int \frac{1}{cos ^{2} ( x ) + sin ^{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

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\int - 9 x^{2} d x

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