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Popular >

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{x ^{6}}{6}

= \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

Popular Examples

integral of (3x^2+4)/((x-2)^2)

\int \frac{3 x ^{2} + 4}{( x - 2 ) ^{2}} d x

integral of 4/((4x-5)ln(4x-5))

\int \frac{4}{( 4 x - 5 ) ln ( 4 x - 5 )} d x

integral of 8/(sqrt(x+1)+\sqrt{x)}

\int \frac{8}{x + 1 + x} d x

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

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

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

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