What is the integral of ((x^2)/((7+x^3)^2)) ?

The integral of ((x^2)/((7+x^3)^2)) is -1/(3(7+x^3))+C

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integral of ((x^2)/((7+x^3)^2))

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

- \frac{1}{3 ( 7 + x ^{3} )} + C

Solution steps

\int \frac{x ^{2}}{( 7 + 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 = 7 + x^{3}

= \frac{1}{3} (- \frac{1}{7 + x ^{3}})

Simplify

\frac{1}{3} (- \frac{1}{7 + x ^{3}}) : - \frac{1}{3 ( 7 + x ^{3} )}

= - \frac{1}{3 ( 7 + x ^{3} )}

Add a constant to the solution

= - \frac{1}{3 ( 7 + x ^{3} )} + C

\frac{\partial}{\partial x} (\frac{x \cdot y}{x - y})

f (x) = - \frac{6 x}{x ^{2} + 1}, at x = 0

x \cdot cos (x)

\frac{\partial}{\partial x} (9 y e^{7 x})

\frac{x + 3}{x - 3}

What is the integral of ((x^2)/((7+x^3)^2)) ?
The integral of ((x^2)/((7+x^3)^2)) is -1/(3(7+x^3))+C