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

The integral of (3x^2+2x^2) is (5x^3)/3+C

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

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

\frac{5 x ^{3}}{3} + C

Solution steps

\int 3 x^{2} + 2 x^{2} d x

Simplify

= \int 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int x^{2} d x

Apply the Power Rule

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

= 5 \cdot \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 x ^{3}}{3}

Add a constant to the solution

= \frac{5 x ^{3}}{3} + C

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