What is the integral of (5+x^8)^48x^7 ?

The integral of (5+x^8)^48x^7 is 1/5 (5+x^8)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5+x^8)^48x^7

\int (5 + x^{8})^{4} 8 x^{7} d x

\frac{1}{5} (5 + x^{8})^{5} + C

Solution steps

\int (5 + x^{8})^{4} \cdot 8 x^{7} d x

Take the constant out:

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

= 8 \cdot \int (5 + x^{8})^{4} x^{7} d x

Apply u-substitution

: \int \frac{( 5 + u ) ^{4}}{8} d u

= 8 \cdot \int \frac{( 5 + u ) ^{4}}{8} d u

Take the constant out:

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

= 8 \cdot \frac{1}{8} \cdot \int (5 + u)^{4} d u

Apply u-substitution

: \int v^{4} d v

= 8 \cdot \frac{1}{8} \cdot \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

= 8 \cdot \frac{1}{8} \cdot \frac{v ^{5}}{5}

Substitute back

= 8 \cdot \frac{1}{8} \cdot \frac{( 5 + x ^{8} ) ^{5}}{5}

Simplify

8 \cdot \frac{1}{8} \cdot \frac{( 5 + x ^{8} ) ^{5}}{5} : \frac{1}{5} (5 + x^{8})^{5}

= \frac{1}{5} (5 + x^{8})^{5}

Add a constant to the solution

= \frac{1}{5} (5 + x^{8})^{5} + C

\int x^{3} sin (3 x) d x

\frac{d y}{d x} + y = e^{- x}

\frac{5 s}{s ^{2} ( s ^{2} + 16 )}

n = 0 \sum \infty n sin (\frac{1}{n})

y = 3 x^{3} - 3 x, (1, 0)

What is the integral of (5+x^8)^48x^7 ?
The integral of (5+x^8)^48x^7 is 1/5 (5+x^8)^5+C