What is the integral of (4x^3-2)^2*x^2 ?

The integral of (4x^3-2)^2*x^2 is 1/36 (4x^3-2)^3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x^3-2)^2*x^2

\int (4 x^{3} - 2)^{2} \cdot x^{2} d x

\frac{1}{36} (4 x^{3} - 2)^{3} + C

Solution steps

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

Apply u-substitution

: \int \frac{u ^{2}}{12} d u

= \int \frac{u ^{2}}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{1}{12} \cdot \frac{u ^{3}}{3}

Substitute back

u = 4 x^{3} - 2

= \frac{1}{12} \cdot \frac{( 4 x ^{3} - 2 ) ^{3}}{3}

Simplify

\frac{1}{12} \cdot \frac{( 4 x ^{3} - 2 ) ^{3}}{3} : \frac{1}{36} (4 x^{3} - 2)^{3}

= \frac{1}{36} (4 x^{3} - 2)^{3}

Add a constant to the solution

= \frac{1}{36} (4 x^{3} - 2)^{3} + C

\int \frac{- 7 ln ( x )}{x} d x

\int (sec^{2} (x) tan^{2} (x)) d x

\int (\frac{1}{cos ^{2} ( x )} - 1) d cos (x) d x

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

\int 3 3 x^{2} d x

What is the integral of (4x^3-2)^2*x^2 ?
The integral of (4x^3-2)^2*x^2 is 1/36 (4x^3-2)^3+C