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Popular >

integral of (1+x)^n

Solution

\int (1 + x)^{n} d x

Solution

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

Solution steps

\int (1 + x)^{n} d x

Apply u-substitution

: \int u^{n} d u

= \int u^{n} d u

Apply the Power Rule

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

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

Substitute back

u = 1 + x

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

Add a constant to the solution

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

Popular Examples

integral of 8x^6

\int 8 x^{6} d x

integral of e^{3x}+sin(x)

\int e^{3 x} + sin (x) d x

integral of 4/(3-2x)

\int \frac{4}{3 - 2 x} d x

integral of e^{-\sqrt[3]{x}}

integral of 1/(sqrt(2x+1)-\sqrt{x)}

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

Frequently Asked Questions (FAQ)

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