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Popular Calculus >

integral of (x^5)/4

Solution

\int \frac{x ^{5}}{4} d x

Solution

\frac{x ^{6}}{24} + C

Solution steps

\int \frac{x ^{5}}{4} 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^{5} d x

Apply the Power Rule

= \frac{1}{4} \cdot \frac{x ^{6}}{6}

Simplify

\frac{1}{4} \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{24}

= \frac{x ^{6}}{24}

Add a constant to the solution

= \frac{x ^{6}}{24} + C

Graph

Popular Examples

integral of 1/(sqrt(4x^2-12x+7))

\int \frac{1}{4 x ^{2} - 12 x + 7} d x

integral of 5/(6+7x^2)

\int \frac{5}{6 + 7 x ^{2}} d x

integral of xe^{-0.2x}

\int x e^{- 0.2 x} d x

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

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

integral of 2-x-x^2

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

Frequently Asked Questions (FAQ)

What is the integral of (x^5)/4 ?
The integral of (x^5)/4 is (x^6)/(24)+C