What is the integral of x(3x^2+1)^4 ?

The integral of x(3x^2+1)^4 is 1/30 (3x^2+1)^5+C

Popular >

integral of x(3x^2+1)^4

\int x (3 x^{2} + 1)^{4} d x

\frac{1}{30} (3 x^{2} + 1)^{5} + C

Solution steps

\int x (3 x^{2} + 1)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{6} d u

= \int \frac{u ^{4}}{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^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

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

Substitute back

u = 3 x^{2} + 1

= \frac{1}{6} \cdot \frac{( 3 x ^{2} + 1 ) ^{5}}{5}

Simplify

\frac{1}{6} \cdot \frac{( 3 x ^{2} + 1 ) ^{5}}{5} : \frac{1}{30} (3 x^{2} + 1)^{5}

= \frac{1}{30} (3 x^{2} + 1)^{5}

Add a constant to the solution

= \frac{1}{30} (3 x^{2} + 1)^{5} + C

\int (\frac{1}{x} + \frac{1}{x ln ( x )}) d x

\int - \frac{cos ( 4 x )}{4} d x

\int \frac{2}{3 - 5 x} d x

\int 16 x^{2} 3 7 - 4 x^{3} d x

\int a cr tan (x) d x

What is the integral of x(3x^2+1)^4 ?
The integral of x(3x^2+1)^4 is 1/30 (3x^2+1)^5+C