What is the integral of ((16x^3))/(x^4+5) ?

The integral of ((16x^3))/(x^4+5) is 4ln|x^4+5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((16x^3))/(x^4+5)

\int \frac{( 16 x ^{3} )}{x ^{4} + 5} d x

4 ln x^{4} + 5 + C

Solution steps

\int \frac{16 x ^{3}}{x ^{4} + 5} d x

Take the constant out:

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

= 16 \cdot \int \frac{x ^{3}}{x ^{4} + 5} d x

Apply u-substitution

: \int \frac{1}{4 u} d u

= 16 \cdot \int \frac{1}{4 u} d u

Take the constant out:

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

= 16 \cdot \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 16 \cdot \frac{1}{4} ln ∣ u ∣

Substitute back

u = x^{4} + 5

= 16 \cdot \frac{1}{4} ln x^{4} + 5

Simplify

16 \cdot \frac{1}{4} ln x^{4} + 5 : 4 ln x^{4} + 5

= 4 ln x^{4} + 5

Add a constant to the solution

= 4 ln x^{4} + 5 + C

\int sin (\frac{2 θ}{3}) d θ

\int 3 x^{- \frac{6}{7}} d x

\int 3 - 4 x d x

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

What is the integral of ((16x^3))/(x^4+5) ?
The integral of ((16x^3))/(x^4+5) is 4ln|x^4+5|+C