What is the integral of tan(12x) ?

The integral of tan(12x) is -1/12 ln|cos(12x)|+C

Popular >

integral of tan(12x)

\int tan (12 x) d x

- \frac{1}{12} ln ∣ cos (12 x) ∣ + C

Solution steps

\int tan (12 x) d x

Rewrite using trig identities

= \int \frac{sin ( 12 x )}{cos ( 12 x )} d x

Apply u-substitution

: \int - \frac{1}{12 u} d u

= \int - \frac{1}{12 u} d u

Take the constant out:

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

= - \frac{1}{12} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{12} ln ∣ u ∣

Substitute back

u = cos (12 x)

= - \frac{1}{12} ln ∣ cos (12 x) ∣

Add a constant to the solution

= - \frac{1}{12} ln ∣ cos (12 x) ∣ + C

\int \frac{9 + 8 x}{1 + x ^{2}} d x

\int sec (2) (x) (1 + tan (x)) d x

\int 6 x e^{4 x} d x

\int \frac{( m - 15 ) x - ( m + 20 )}{3 x ^{2} + x - 4} d x

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

What is the integral of tan(12x) ?
The integral of tan(12x) is -1/12 ln|cos(12x)|+C