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

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

Popular >

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

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

sec (x) + x + C

Solution steps

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

Expand

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

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

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

\int 1 d x = x

= sec (x) + x

Add a constant to the solution

= sec (x) + x + C

f (x) = \frac{6}{x}, (1, 6)

\int e^{x + 3 y} d x

\int \frac{sec ^{4} ( x )}{tan ( x )} d x

y = x^{3} - 6 x, (0, 3)

\int \frac{24}{25 + r ^{2}} d r

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