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Popular >

integral of ax^5

Solution

\int a x^{5} d x

Solution

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

Solution steps

\int a x^{5} d x

Take the constant out:

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

= a \cdot \int x^{5} d x

Apply the Power Rule

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

Graph

Popular Examples

area y=x^2,y=8-x^2,y=4x+11 area

y = x^{2}, y = 8 - x^{2}, y = 4 x + 11

limit as x approaches 3 of (x-2)^2

x \to 3 lim ((x - 2)^{2})

(dy)/(dx)= k/(x^2)

\frac{d y}{d x} = \frac{k}{x ^{2}}

integral from 1 to 2 of (3ln(x))/(x^2)

\int_{1}^{2} \frac{3 ln ( x )}{x ^{2}} d x

(\partial)/(\partial x)(2y^2-3x^2-z)

\frac{\partial}{\partial x} (2 y^{2} - 3 x^{2} - z)

Frequently Asked Questions (FAQ)

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