What is the integral of x^2(1+2x^3)^5 ?

The integral of x^2(1+2x^3)^5 is 1/36 (1+2x^3)^6+C

Popular >

integral of x^2(1+2x^3)^5

\int x^{2} (1 + 2 x^{3})^{5} d x

\frac{1}{36} (1 + 2 x^{3})^{6} + C

Solution steps

\int x^{2} (1 + 2 x^{3})^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{6} d u

= \int \frac{u ^{5}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u^{5} d u

Apply the Power Rule

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

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

Substitute back

u = 1 + 2 x^{3}

= \frac{1}{6} \cdot \frac{( 1 + 2 x ^{3} ) ^{6}}{6}

Simplify

\frac{1}{6} \cdot \frac{( 1 + 2 x ^{3} ) ^{6}}{6} : \frac{1}{36} (1 + 2 x^{3})^{6}

= \frac{1}{36} (1 + 2 x^{3})^{6}

Add a constant to the solution

= \frac{1}{36} (1 + 2 x^{3})^{6} + C

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

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

\frac{d}{d x} (\frac{x}{2} - \frac{2}{x})

\frac{d}{d x} ((5 + 3 x)^{5})

x \to \infty lim (- 3 x + x)

What is the integral of x^2(1+2x^3)^5 ?
The integral of x^2(1+2x^3)^5 is 1/36 (1+2x^3)^6+C