What is the integral of 4x(x^2+5)^3 ?

The integral of 4x(x^2+5)^3 is 1/2 (x^2+5)^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x(x^2+5)^3

\int 4 x (x^{2} + 5)^{3} d x

\frac{1}{2} (x^{2} + 5)^{4} + C

Solution steps

\int 4 x (x^{2} + 5)^{3} d x

Take the constant out:

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

= 4 \cdot \int x (x^{2} + 5)^{3} d x

Apply u-substitution

: \int \frac{u ^{3}}{2} d u

= 4 \cdot \int \frac{u ^{3}}{2} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= 4 \cdot \frac{1}{2} \cdot \frac{u ^{4}}{4}

Substitute back

u = x^{2} + 5

= 4 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{4}}{4}

Simplify

4 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{4}}{4} : \frac{1}{2} (x^{2} + 5)^{4}

= \frac{1}{2} (x^{2} + 5)^{4}

Add a constant to the solution

= \frac{1}{2} (x^{2} + 5)^{4} + C

h \to 0 lim (x^{2} + 3 x h)

\int \frac{y ^{2} - 16}{y} d y

f (x) = ln (1 - x^{2})

\frac{d}{d x} (x e^{2 x + 1})

n = 1 \sum \infty 2 0^{n} x^{n} n!

What is the integral of 4x(x^2+5)^3 ?
The integral of 4x(x^2+5)^3 is 1/2 (x^2+5)^4+C