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Popular >

integral of (x^5)/6

Solution

\int \frac{x ^{5}}{6} d x

Solution

\frac{x ^{6}}{36} + C

Solution steps

\int \frac{x ^{5}}{6} d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

\frac{1}{6} \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{36}

= \frac{x ^{6}}{36}

Add a constant to the solution

= \frac{x ^{6}}{36} + C

Popular Examples

limit as x approaches 0 of ln(1-9x)

x \to 0 lim (ln (1 - 9 x))

limit as x approaches 6 of 7/((x-6)^2)

x \to 6 lim (\frac{7}{( x - 6 ) ^{2}})

(d^2)/(dx^2)(2sqrt(x))

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

integral of cos^{-2}(2x)

\int cos^{- 2} (2 x) d x

sum from n=0 to infinity of 1/(5^n)

n = 0 \sum \infty \frac{1}{5 ^{n}}

Frequently Asked Questions (FAQ)

What is the integral of (x^5)/6 ?
The integral of (x^5)/6 is (x^6)/(36)+C