What is the integral of tan(6x) ?

The integral of tan(6x) is -1/6 ln|cos(6x)|+C

Popular >

integral of tan(6x)

\int tan (6 x) d x

- \frac{1}{6} ln ∣ cos (6 x) ∣ + C

Solution steps

\int tan (6 x) d x

Rewrite using trig identities

= \int \frac{sin ( 6 x )}{cos ( 6 x )} d x

Apply u-substitution

: \int - \frac{1}{6 u} d u

= \int - \frac{1}{6 u} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{6} ln ∣ u ∣

Substitute back

u = cos (6 x)

= - \frac{1}{6} ln ∣ cos (6 x) ∣

Add a constant to the solution

= - \frac{1}{6} ln ∣ cos (6 x) ∣ + C

\frac{d}{d x} (2 e^{x - 5})

y = - 9 x^{2}

n = 1 \sum \infty \frac{( - 1 ) ^{n - 1} n ^{2}}{1 0 ^{n}}

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

\frac{d}{d x} (sin (3 x^{4}))