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Popular >

integral of (x-1)^n

Solution

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

Solution

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

Solution steps

\int (x - 1)^{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 = x - 1

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

Add a constant to the solution

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

Popular Examples

integral of 1/(-x^2+1)

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

derivative of 9xln(x)

\frac{d}{d x} (9 x ln (x))

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2^{- x}

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x \to 400 - lim (x)

integral of (x^5)/(sqrt(4+x^2))

\int \frac{x ^{5}}{4 + x ^{2}} d x

Frequently Asked Questions (FAQ)

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