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Popular >

integral of nx^n

Solution

\int n x^{n} d x

Solution

\frac{n x ^{n + 1}}{n + 1} + C

Solution steps

\int n x^{n} 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} d x

Apply the Power Rule

: \frac{x ^{n + 1}}{n + 1}

= n \frac{x ^{n + 1}}{n + 1}

Multiply fractions:

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

= \frac{n x ^{n + 1}}{n + 1}

Add a constant to the solution

= \frac{n x ^{n + 1}}{n + 1} + C

Popular Examples

integral of 1/(x^2sqrt(3-x^2))

\int \frac{1}{x ^{2} 3 - x ^{2}} d x

limit as x approaches infinity of-2x

x \to \infty lim (- 2 x)

(sqrt(2x^4+1))/y (dy)/(dx)+1/6 y^3x^3=0

\frac{2 x ^{4} + 1}{y} \frac{d y}{d x} + \frac{1}{6} y^{3} x^{3} = 0

derivative of 1/(2x)derivative of

\frac{1}{2 x}

integral of pix^2

\int π x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of nx^n ?
The integral of nx^n is (nx^{n+1})/(n+1)+C