What is the integral of (x^5)/(x^6+1) ?

The integral of (x^5)/(x^6+1) is 1/6 ln|x^6+1|+C

Popular >

integral of (x^5)/(x^6+1)

\int \frac{x ^{5}}{x ^{6} + 1} d x

\frac{1}{6} ln x^{6} + 1 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} + 1} 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 = x^{6} + 1

= \frac{1}{6} ln x^{6} + 1

Add a constant to the solution

= \frac{1}{6} ln x^{6} + 1 + C

\frac{d}{d x} (10 ln (x))

\frac{d}{d x} (\frac{x + 1}{x + 5})

\frac{\partial}{\partial x} (x^{2} e^{7 x y})

\int 2 x (x^{2} + 2)^{9} d x

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (e^{u (v) v})

What is the integral of (x^5)/(x^6+1) ?
The integral of (x^5)/(x^6+1) is 1/6 ln|x^6+1|+C