What is the integral of (6x^5+6)/((x^6+6x)^2) ?

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

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integral of (6x^5+6)/((x^6+6x)^2)

\int \frac{6 x ^{5} + 6}{( x ^{6} + 6 x ) ^{2}} d x

- \frac{1}{x ^{6} + 6 x} + C

Solution steps

\int \frac{6 x ^{5} + 6}{( x ^{6} + 6 x ) ^{2}} d x

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x^{6} + 6 x

= - \frac{1}{x ^{6} + 6 x}

Add a constant to the solution

= - \frac{1}{x ^{6} + 6 x} + C

n = 0 \sum \infty 2 e^{- n}

\frac{\partial}{\partial x} (9 - x^{2})

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

x \to 0 lim (\frac{3}{x} + \frac{3}{x ^{2} - x})

\frac{d}{d x} (2 x + sin (x))

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