What is the integral of (3x^7)/(4+x^8) ?

The integral of (3x^7)/(4+x^8) is 3/8 ln|4+x^8|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x^7)/(4+x^8)

\int \frac{3 x ^{7}}{4 + x ^{8}} d x

\frac{3}{8} ln 4 + x^{8} + C

Solution steps

\int \frac{3 x ^{7}}{4 + x ^{8}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x ^{7}}{4 + x ^{8}} d x

Apply u-substitution

: \int \frac{1}{8 u} d u

= 3 \cdot \int \frac{1}{8 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{8} ln ∣ u ∣

Substitute back

u = 4 + x^{8}

= 3 \cdot \frac{1}{8} ln 4 + x^{8}

Simplify

3 \cdot \frac{1}{8} ln 4 + x^{8} : \frac{3}{8} ln 4 + x^{8}

= \frac{3}{8} ln 4 + x^{8}

Add a constant to the solution

= \frac{3}{8} ln 4 + x^{8} + C

f (x) = 5 lo g_{10} (4 x^{2})

\frac{d}{d x} (sin^{4} (2 x) cos^{4} (3 x))

\frac{384 x}{x ^{2} + 289}

2 x^{2} + 3 x

\int_{0}^{1.2} (1 - \frac{y}{2}) d y

What is the integral of (3x^7)/(4+x^8) ?
The integral of (3x^7)/(4+x^8) is 3/8 ln|4+x^8|+C