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Popular Calculus >

integral of (1+x)^n

Solution

integral

(1 + x)^{n}

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

Apply the Power Rule

= \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

Graph

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in t e g r a l \frac{1}{( ( x + 1 ) ( x - 2 ) )}

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