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

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

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

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

\frac{x ^{3}}{3 a ^{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{a ^{2}} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{a ^{2}} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 a ^{2}}

= \frac{x ^{3}}{3 a ^{2}}

Add a constant to the solution

= \frac{x ^{3}}{3 a ^{2}} + C

\int 2 x \cdot e^{4 x + 2} d x

(t^{2} + t) cos (5 t)

y^{^{''}} + 4 y^{^{'}} + 4 y = - 3 e^{2 t}

n = 1 \sum \infty \frac{1}{2 ^{n + 2}}

f (x) = 18 e^{x} + 10 x, at x = 0

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