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Popular >

integral of ax^{a-1}

Solution

\int a x^{a - 1} d x

Solution

x^{a} + C

Solution steps

\int a x^{a - 1} d x

Take the constant out:

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

= a \cdot \int x^{a - 1} d x

Apply the Power Rule

: \frac{x ^{a}}{a}

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

Simplify

a \frac{x ^{a}}{a} : x^{a}

= x^{a}

Add a constant to the solution

= x^{a} + C

Graph

Popular Examples

integral of x/((sqrt(x^2+1)))

\int \frac{x}{( x ^{2} + 1 )} d x

integral of 5ln(x^2-x+6)

\int 5 ln (x^{2} - x + 6) d x

integral of e^x+9/x-4

\int e^{x} + \frac{9}{x} - 4 d x

integral of (2x)/((x^2+2x+5)^2)

\int \frac{2 x}{( x ^{2} + 2 x + 5 ) ^{2}} d x

integral of (a-bx^2)

\int (a - b x^{2}) d x

Frequently Asked Questions (FAQ)

What is the integral of ax^{a-1} ?
The integral of ax^{a-1} is x^a+C