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Popular >

integral of (3x^2)/2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(3x^{1/3}y^{2/3})

\frac{\partial}{\partial x} (3 x^{\frac{1}{3}} y^{\frac{2}{3}})

limit as x approaches 0 of 7/(1+e^{1/x)}

x \to 0 lim (\frac{7}{1 + e ^{\frac{1}{x}}})

integral of 1/(7xlog_{3)(x)}

\int \frac{1}{7 x lo g _{3} ( x )} d x

limit as x approaches 2 of 2x^2+4x-5

x \to 2 lim (2 x^{2} + 4 x - 5)

integral from 0 to 4 of 400-20t

\int_{0}^{4} 400 - 20 t d t

Frequently Asked Questions (FAQ)

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