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Popular >

integral of (x^6)/6

Solution

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

Solution

\frac{x ^{7}}{42} + C

Solution steps

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

Apply the Power Rule

: \frac{x ^{7}}{7}

= \frac{1}{6} \cdot \frac{x ^{7}}{7}

Simplify

\frac{1}{6} \cdot \frac{x ^{7}}{7} : \frac{x ^{7}}{42}

= \frac{x ^{7}}{42}

Add a constant to the solution

= \frac{x ^{7}}{42} + C

Popular Examples

integral from 2 to 8 of x

\int_{2}^{8} x d x

integral of cos^3(xsi)n^4x

\int cos^{3} (x s i) n^{4} x d x

integral of (x^3)/(324)

\int \frac{x ^{3}}{324} d x

integral from 0 to infinity of x/(1+x^3)

\int_{0}^{\infty} \frac{x}{1 + x ^{3}} d x

limit as x approaches 4 of x^2

x \to 4 lim (x^{2})

Frequently Asked Questions (FAQ)

What is the integral of (x^6)/6 ?
The integral of (x^6)/6 is (x^7)/(42)+C