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Popular >

integral of kx^n

Solution

\int k x^{n} d x

Solution

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

Solution steps

\int k x^{n} d x

Take the constant out:

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

= k \cdot \int x^{n} d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (sin^2(x))/(1+cos(2x))

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

integral of (t^2)/(1+t)

\int \frac{t ^{2}}{1 + t} d t

integral of (x^3+4x^2-x)

\int (x^{3} + 4 x^{2} - x) d x

integral of-1/(t+1)

\int - \frac{1}{t + 1} d t

integral of-ln^2(x)

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

Frequently Asked Questions (FAQ)

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