What is the integral of x^2(x^3+5)^7 ?

The integral of x^2(x^3+5)^7 is 1/24 (x^3+5)^8+C

Popular >

integral of x^2(x^3+5)^7

\int x^{2} (x^{3} + 5)^{7} d x

\frac{1}{24} (x^{3} + 5)^{8} + C

Solution steps

\int x^{2} (x^{3} + 5)^{7} d x

Apply u-substitution

: \int \frac{u ^{7}}{3} d u

= \int \frac{u ^{7}}{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^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{1}{3} \cdot \frac{u ^{8}}{8}

Substitute back

u = x^{3} + 5

= \frac{1}{3} \cdot \frac{( x ^{3} + 5 ) ^{8}}{8}

Simplify

\frac{1}{3} \cdot \frac{( x ^{3} + 5 ) ^{8}}{8} : \frac{1}{24} (x^{3} + 5)^{8}

= \frac{1}{24} (x^{3} + 5)^{8}

Add a constant to the solution

= \frac{1}{24} (x^{3} + 5)^{8} + C

\frac{d}{d x} (x^{12} - 12 e^{x})

f (x) = e^{- 1}

f (x) = x^{8}

\int sin (- 4 x) cos (3 x) d x

\frac{\partial}{\partial y} (e^{x} (x - y)^{2})

What is the integral of x^2(x^3+5)^7 ?
The integral of x^2(x^3+5)^7 is 1/24 (x^3+5)^8+C