What is the integral of cos(x)tan(sin(x)) ?

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

Popular >

integral of cos(x)tan(sin(x))

\int cos (x) tan (sin (x)) d x

- ln ∣ cos (sin (x)) ∣ + C

Solution steps

\int cos (x) tan (sin (x)) d x

Apply u-substitution

: \int tan (u) d u

= \int tan (u) d u

Rewrite using trig identities

= \int \frac{sin ( u )}{cos ( u )} d u

Apply u-substitution

: \int - \frac{1}{v} d v

= \int - \frac{1}{v} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= - ln ∣ v ∣

Substitute back

= - ln ∣ cos (sin (x)) ∣

Add a constant to the solution

= - ln ∣ cos (sin (x)) ∣ + C

\int - 7 x^{3} e^{x^{2}} d x

\int \frac{1}{4 x ^{2} + 4 x + 1} d x

\int \frac{x ^{2} - 4 x - 3}{3 x ^{3} + 17 x ^{2} - 6 x} d x

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

\int \frac{x + 1}{2} d x

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