What is the integral of (x^5)/(x^6+4) ?

The integral of (x^5)/(x^6+4) is 1/6 ln|x^6+4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^5)/(x^6+4)

\int \frac{x ^{5}}{x ^{6} + 4} d x

\frac{1}{6} ln x^{6} + 4 + C

Solution steps

\int \frac{x ^{5}}{x ^{6} + 4} 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} + 4

= \frac{1}{6} ln x^{6} + 4

Add a constant to the solution

= \frac{1}{6} ln x^{6} + 4 + C

n = 0 \sum \infty \frac{1}{4 n + 1}

\int \frac{1}{e ^{x}} d x

y^{^{''}} + 4 y^{^{'}} + 2 y = 0

\frac{\partial}{\partial u} (tan (\frac{u}{v}))

\int \frac{x}{( 3 x ^{2} - 4 ) ^{2}} d x

What is the integral of (x^5)/(x^6+4) ?
The integral of (x^5)/(x^6+4) is 1/6 ln|x^6+4|+C