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

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

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integral of (3x^2)/x

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

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

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{x ^{2}}{x} d x

Cancel the common factor:

x

= 3 \cdot \int x d x

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

\int_{0}^{1} \frac{6}{x ^{2} + 2 x - 8} d x

\int \frac{- x - 2}{3 ( x ^{2} + x + 1 )} d x

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

12 y^{^{''}} - 5 y^{^{'}} - 2 y = 0

y^{^{'}} = 7 y^{2}