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

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

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integral of (2-sin^2(x))/(cos^2(x))

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

x + tan (x) + C

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

= x + tan (x)

Add a constant to the solution

= x + tan (x) + C

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