What is the integral of (sin(5x))/(1-cos(5x)) ?

The integral of (sin(5x))/(1-cos(5x)) is 1/5 ln|1-cos(5x)|+C

Popular >

integral of (sin(5x))/(1-cos(5x))

\int \frac{sin ( 5 x )}{1 - cos ( 5 x )} d x

\frac{1}{5} ln ∣ 1 - cos (5 x) ∣ + C

Solution steps

\int \frac{sin ( 5 x )}{1 - cos ( 5 x )} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 1 - cos (5 x)

= \frac{1}{5} ln ∣ 1 - cos (5 x) ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 1 - cos (5 x) ∣ + C

\frac{d y}{( 1 + 4 y ^{2} )} = - \frac{x}{( 1 + x ^{4} )} d x

6 x^{\frac{3}{2}}

x \to \infty lim (0.9 9^{x})

\frac{d}{d t} (a t e^{t})

3 x y^{2} y^{^{'}} + 3 y^{3} = 1

What is the integral of (sin(5x))/(1-cos(5x)) ?
The integral of (sin(5x))/(1-cos(5x)) is 1/5 ln|1-cos(5x)|+C