What is the integral of (x^2)/(4a+2a) ?

The integral of (x^2)/(4a+2a) is (x^3)/(18a)+C

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integral of (x^2)/(4a+2a)

integral

\frac{x ^{2}}{4 a + 2 a}

\frac{x ^{3}}{18 a} + C

Solution steps

\int \frac{x ^{2}}{4 a + 2 a} d x

Take the constant out:

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

= \frac{1}{4 a + 2 a} \cdot \int x^{2} d x

Simplify

= \frac{1}{6 a} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{6 a} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{6 a} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{18 a}

= \frac{x ^{3}}{18 a}

Add a constant to the solution

= \frac{x ^{3}}{18 a} + C

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

\frac{1}{( x ^{2} - 4 )}

\frac{4 x ^{4}}{( 1 + x ^{2} )}

\frac{4 t}{3 t ^{2} - 7}

u^{\frac{1}{2}}

What is the integral of (x^2)/(4a+2a) ?
The integral of (x^2)/(4a+2a) is (x^3)/(18a)+C