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Popular >

integral of 5x^2*x

Solution

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

Solution

\frac{5 x ^{4}}{4} + C

Solution steps

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

Simplify

x^{2} x : x^{3}

= 5 \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= 5 \cdot \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{5 x ^{4}}{4}

Add a constant to the solution

= \frac{5 x ^{4}}{4} + C

Graph

Popular Examples

integral of (3x^2)/(2(9x^2+1))

\int \frac{3 x ^{2}}{2 ( 9 x ^{2} + 1 )} d x

integral of (e^{2t})/t

\int \frac{e ^{2 t}}{t} d t

integral of 12x^3+1/(6sqrt(x))-3/(2x^4)

\int 12 x^{3} + \frac{1}{6 x} - \frac{3}{2 x ^{4}} d x

integral of (x^{(-1)/3})

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

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

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

Frequently Asked Questions (FAQ)

What is the integral of 5x^2*x ?
The integral of 5x^2*x is (5x^4)/4+C