What is the integral of x^2(x^3+1)^9 ?

The integral of x^2(x^3+1)^9 is 1/30 (x^3+1)^{10}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2(x^3+1)^9

\int x^{2} (x^{3} + 1)^{9} d x

\frac{1}{30} (x^{3} + 1)^{10} + C

Solution steps

\int x^{2} (x^{3} + 1)^{9} d x

Apply u-substitution

: \int \frac{u ( u ^{\frac{3}{2}} + 1 ) ^{9}}{2 x} d u

= \int \frac{( u + 1 ) ^{9}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int (u + 1)^{9} d u

Apply u-substitution

: \int v^{9} d v

= \frac{1}{3} \cdot \int v^{9} d v

Apply the Power Rule

: \frac{v ^{10}}{10}

= \frac{1}{3} \cdot \frac{v ^{10}}{10}

Substitute back

= \frac{1}{3} \cdot \frac{( x ^{3} + 1 ) ^{10}}{10}

Simplify

\frac{1}{3} \cdot \frac{( x ^{3} + 1 ) ^{10}}{10} : \frac{1}{30} (x^{3} + 1)^{10}

= \frac{1}{30} (x^{3} + 1)^{10}

Add a constant to the solution

= \frac{1}{30} (x^{3} + 1)^{10} + C

\int e^{y + x} d y

\int sin^{4} (a) x d x

\int \frac{4000}{( 1 + 0.4 x ) ^{2}} d x

\int 27 x sin (3 x) d x

\int \frac{cos ( y )}{sin ( y ) - 1} d y

What is the integral of x^2(x^3+1)^9 ?
The integral of x^2(x^3+1)^9 is 1/30 (x^3+1)^{10}+C