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Popular >

integral of au

Solution

\int a u d u

Solution

\frac{a u ^{2}}{2} + C

Solution steps

\int a u d u

Take the constant out:

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

= a \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= a \frac{u ^{2}}{2}

Multiply fractions:

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

= \frac{a u ^{2}}{2}

Add a constant to the solution

= \frac{a u ^{2}}{2} + C

Graph

Popular Examples

integral of (x-7)/(x^2+16)

\int \frac{x - 7}{x ^{2} + 16} d x

integral of 7/((x-3)^2)

\int \frac{7}{( x - 3 ) ^{2}} d x

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

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

integral of sec^5(u)

\int sec^{5} (u) d u

integral of xye^{x^2+y^2}

\int x y e^{x^{2} + y^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of au ?
The integral of au is (au^2)/2+C