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

The integral of (x^2)/((3+x^3)^2) is -1/(3(3+x^3))+C

Popular >

integral of (x^2)/((3+x^3)^2)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u ^{2}} d u

= \int \frac{1}{3 u ^{2}} 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 \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= \frac{1}{3} (- \frac{1}{u})

Substitute back

u = 3 + x^{3}

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

Simplify

\frac{1}{3} (- \frac{1}{3 + x ^{3}}) : - \frac{1}{3 ( 3 + x ^{3} )}

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

Add a constant to the solution

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

\frac{4}{( s ^{2} - 9 )}

\int_{1}^{2} \frac{1}{x} - \frac{1}{x ^{2}} d x

\int \frac{y}{y ^{2} + 2 y + 1} d y

x \to 0 lim (6 x - 1)

\int \frac{- 3}{x ^{2} x ^{2} - 9} d x

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