What is the integral of 1/(x^{8/9)(8+x^{1/9})} ?

The integral of 1/(x^{8/9)(8+x^{1/9})} is 9ln|8+x^{1/9}|+C

Popular >

integral of 1/(x^{8/9)(8+x^{1/9})}

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

9 ln 8 + x^{\frac{1}{9}} + C

Solution steps

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

Apply u-substitution

: \int \frac{9}{u} d u

= \int \frac{9}{u} d u

Take the constant out:

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

= 9 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 ln ∣ u ∣

Substitute back

u = 8 + x^{\frac{1}{9}}

= 9 ln 8 + x^{\frac{1}{9}}

Add a constant to the solution

= 9 ln 8 + x^{\frac{1}{9}} + C

\int 4 x^{2} sec (5 x^{3}) d x

\int_{0}^{\frac{π}{4}} 3 tan^{3} (x) d x

\frac{d}{d x} (4 arccot (\frac{x}{2}))

\int \frac{2 x - 1}{x ^{2} - 6 x + 18} d x

\frac{\partial}{\partial z} (e^{3 x + 4 y} cos (5 z))

What is the integral of 1/(x^{8/9)(8+x^{1/9})} ?
The integral of 1/(x^{8/9)(8+x^{1/9})} is 9ln|8+x^{1/9}|+C