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Popular >

integral of nx^{n-1}

Solution

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

Solution

x^{n} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{n}}{n}

= n \frac{x ^{n}}{n}

Simplify

n \frac{x ^{n}}{n} : x^{n}

= x^{n}

Add a constant to the solution

= x^{n} + C

Popular Examples

1/4 y^{''}+y^'+y=x^2-3x

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} - 3 x

y'=(e^{3*x}+3*x*y+y)/x

y^{'} = \frac{e ^{3 \cdot x} + 3 \cdot x \cdot y + y}{x}

integral of 1/(2-7x)

\int \frac{1}{2 - 7 x} d x

derivative of 1/(\sqrt[3]{x^5})

derivative of sin((pix)^9)derivative of

sin ((π x)^{9})

Frequently Asked Questions (FAQ)

What is the integral of nx^{n-1} ?
The integral of nx^{n-1} is x^n+C