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Popular >

integral of 1/4 x^3

Solution

\int \frac{1}{4} x^{3} d x

Solution

\frac{x ^{4}}{16} + C

Solution steps

\int \frac{1}{4} x^{3} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int x^{3} d x

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{x ^{4}}{4}

Simplify

\frac{1}{4} \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{16}

= \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{x ^{4}}{16} + C

Graph

Popular Examples

integral of ((sqrt(x)-x^3e^x+x^2)/(x^3))

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

y^'=sqrt((1-y^2)/(e^x))

y^{^{'}} = \frac{1 - y ^{2}}{e ^{x}}

sum from n=0 to infinity of p^n

n = 0 \sum \infty p^{n}

limit as x approaches 3 of 6x

x \to 3 lim (6 x)

integral of q/(pi(-0.125x+0.03125)^2)

\int \frac{q}{π ( - 0.125 x + 0.03125 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/4 x^3 ?
The integral of 1/4 x^3 is (x^4)/(16)+C