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

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

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

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

- cot (x) + 2 tan (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{sin ^{2} ( x )} d x = - cot (x)

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

= - cot (x) + 2 tan (x)

Add a constant to the solution

= - cot (x) + 2 tan (x) + C

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