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

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

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

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

tan (x) + x + C

Solution steps

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

Expand

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

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

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

\int 1 d x = x

= tan (x) + x

Add a constant to the solution

= tan (x) + x + C

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

\int 3 x^{2} + 2 x - 1 d x

\frac{d}{d x} (3 x^{2} - x + 5)

sin^{6} (x)

\int_{0}^{\frac{1}{3}} 2 arcsin (3 y) d y

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