What is the integral of (x+5)^{10} ?

The integral of (x+5)^{10} is ((x+5)^{11})/(11)+C

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integral of (x+5)^{10}

\int (x + 5)^{10} d x

\frac{( x + 5 ) ^{11}}{11} + C

Solution steps

\int (x + 5)^{10} d x

Apply u-substitution

: \int u^{10} d u

= \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= \frac{u ^{11}}{11}

Substitute back

u = x + 5

= \frac{( x + 5 ) ^{11}}{11}

Add a constant to the solution

= \frac{( x + 5 ) ^{11}}{11} + C

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What is the integral of (x+5)^{10} ?
The integral of (x+5)^{10} is ((x+5)^{11})/(11)+C