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

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

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

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

- 2 cos (x) + x + C

Solution steps

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

Expand

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

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

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

\int 1 d x = x

= - 2 cos (x) + x

Add a constant to the solution

= - 2 cos (x) + x + C

\int \frac{1}{( 25 x ^{2} + 1 ) ^{2}} d x

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

\int e^{0.1 t} d t

\int [arcsin (x)]^{2} d x

\int (3 x^{2} + y) d x

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