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

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

Popular >

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{u ^{5}}{3} d u

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

Apply the Power Rule

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

= \frac{1}{3} \cdot \frac{u ^{6}}{6}

Substitute back

u = x^{3} + 1

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{2 x ^{3} - 1}{x + 2} d x

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

\int sec (x) (4 sec (x) + 7 tan (x)) d x

\int (3 x^{2} + 6 x)^{51} (x + 1) d x

\int sin (\frac{π x}{y}) d x

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