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Popular >

integral of (x^5)/5

Solution

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

Solution

\frac{x ^{6}}{30} + C

Solution steps

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

Take the constant out:

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

= \frac{1}{5} \cdot \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= \frac{1}{5} \cdot \frac{x ^{6}}{6}

Simplify

\frac{1}{5} \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{30}

= \frac{x ^{6}}{30}

Add a constant to the solution

= \frac{x ^{6}}{30} + C

Popular Examples

limit as x approaches infinity of (4^x)/(3^{x-1)}

x \to \infty lim (\frac{4 ^{x}}{3 ^{x - 1}})

integral of \sqrt[3]{8x}

(\partial)/(\partial x)(y/(y^2+x^2))

\frac{\partial}{\partial x} (\frac{y}{y ^{2} + x ^{2}})

derivative of (2x^3-x^2+5x/(x^2-25))

\frac{d}{d x} (\frac{2 x ^{3} - x ^{2} + 5 x}{x ^{2} - 25})

integral of (6-y)/(y-1)

\int \frac{6 - y}{y - 1} d y

Frequently Asked Questions (FAQ)

What is the integral of (x^5)/5 ?
The integral of (x^5)/5 is (x^6)/(30)+C