What is the integral of x(x^2-2)^5 ?

The integral of x(x^2-2)^5 is 1/12 (x^2-2)^6+C

Popular >

integral of x(x^2-2)^5

\int x (x^{2} - 2)^{5} d x

\frac{1}{12} (x^{2} - 2)^{6} + C

Solution steps

\int x (x^{2} - 2)^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{2} d u

= \int \frac{u ^{5}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{5} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Substitute back

u = x^{2} - 2

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

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} - 2 ) ^{6}}{6} : \frac{1}{12} (x^{2} - 2)^{6}

= \frac{1}{12} (x^{2} - 2)^{6}

Add a constant to the solution

= \frac{1}{12} (x^{2} - 2)^{6} + C

\int \frac{5 y ^{2} + 6 y}{10 y + 3} d y

\int \frac{8}{3 x ^{3}} d x

e^{4 x}

\int tan (5 x) sec^{4} (5 x) d x

\int \frac{5 x ^{3} - 8 x + 5}{x ^{3} - x ^{2}} d x

What is the integral of x(x^2-2)^5 ?
The integral of x(x^2-2)^5 is 1/12 (x^2-2)^6+C