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

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

Popular >

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

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

- ln ∣ cos (x) ∣ + x + C

Solution steps

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

Expand

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

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

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

\int 1 d x = x

= - ln ∣ cos (x) ∣ + x

Add a constant to the solution

= - ln ∣ cos (x) ∣ + x + C

\int \frac{x - 4}{x ^{3} - x ^{2} - x - 2} d x

\int 64 x x^{2} + 4 d x

\int ln (x) \frac{1}{x} d x

\int \frac{15}{( 0.5 x + 1 ) ^{2}} d x

\int (2 - 3 x)^{7} d x

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