What is the integral of (x^9)/(x^5+5) ?

The integral of (x^9)/(x^5+5) is (x^5)/5-ln|x^5+5|+C

Popular >

integral of (x^9)/(x^5+5)

\int \frac{x ^{9}}{x ^{5} + 5} d x

\frac{x ^{5}}{5} - ln x^{5} + 5 + C

Solution steps

\int \frac{x ^{9}}{x ^{5} + 5} d x

Long division

\frac{x ^{9}}{x ^{5} + 5} : x^{4} - \frac{5 x ^{4}}{x ^{5} + 5}

= \int x^{4} - \frac{5 x ^{4}}{x ^{5} + 5} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{4} d x - \int \frac{5 x ^{4}}{x ^{5} + 5} d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int \frac{5 x ^{4}}{x ^{5} + 5} d x = ln x^{5} + 5

= \frac{x ^{5}}{5} - ln x^{5} + 5

Add a constant to the solution

= \frac{x ^{5}}{5} - ln x^{5} + 5 + C

\int \frac{( x + 5 ) ^{5}}{2 x} d x

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

\int (y e^{y} + 2) d y

\int \frac{e 5 x + 1}{5 x + 1} d x

\int \frac{1}{3 x ^{\frac{2}{3}}} d x

What is the integral of (x^9)/(x^5+5) ?
The integral of (x^9)/(x^5+5) is (x^5)/5-ln|x^5+5|+C