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

The integral of 4x^2(4x^3+5)^5 is 1/18 (4x^3+5)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{18} (4 x^{3} + 5)^{6} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{u ^{5}}{12} d u

= 4 \cdot \int \frac{u ^{5}}{12} d u

Take the constant out:

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

= 4 \cdot \frac{1}{12} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 4 \cdot \frac{1}{12} \cdot \frac{u ^{6}}{6}

Substitute back

u = 4 x^{3} + 5

= 4 \cdot \frac{1}{12} \cdot \frac{( 4 x ^{3} + 5 ) ^{6}}{6}

Simplify

4 \cdot \frac{1}{12} \cdot \frac{( 4 x ^{3} + 5 ) ^{6}}{6} : \frac{1}{18} (4 x^{3} + 5)^{6}

= \frac{1}{18} (4 x^{3} + 5)^{6}

Add a constant to the solution

= \frac{1}{18} (4 x^{3} + 5)^{6} + C

ln (3 \frac{3 x}{x + 2})

\int - z^{2} d z

\frac{\partial}{\partial x} (y \cdot e^{\frac{x}{y}})

x \to 0 lim (\frac{sin ( 2 x ) sin ( 3 x )}{sin ( 2 x ) sin ( 3 x )})

\frac{d x}{d t} - 5 x = sin (2 t)

What is the integral of 4x^2(4x^3+5)^5 ?
The integral of 4x^2(4x^3+5)^5 is 1/18 (4x^3+5)^6+C