What is the integral of tan(2x) ?

The integral of tan(2x) is -1/2 ln|cos(2x)|+C

Popular >

integral of tan(2x)

\int tan (2 x) d x

- \frac{1}{2} ln ∣ cos (2 x) ∣ + C

Solution steps

\int tan (2 x) d x

Rewrite using trig identities

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

Apply u-substitution

: \int - \frac{1}{2 u} d u

= \int - \frac{1}{2 u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} ln ∣ u ∣

Substitute back

u = cos (2 x)

= - \frac{1}{2} ln ∣ cos (2 x) ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

\frac{\partial}{\partial z} (6 y (z + 1)^{4})

\int (1 - 2 x) d x

x \to - \infty lim (1 x)

y = x^{2} + 1, y = 5

f (x) = 7 x^{2} - x^{3}, (1, 6)