What is the integral of (x^2+2x+1)^{10} ?

The integral of (x^2+2x+1)^{10} is ((x+1)^{21})/(21)+C

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integral of (x^2+2x+1)^{10}

\int (x^{2} + 2 x + 1)^{10} d x

\frac{( x + 1 ) ^{21}}{21} + C

Solution steps

\int (x^{2} + 2 x + 1)^{10} d x

Complete the square

x^{2} + 2 x + 1 : (x + 1)^{2}

= \int ((x + 1)^{2})^{10} d x

Apply u-substitution

: \int u^{20} d u

= \int u^{20} d u

Apply the Power Rule

: \frac{u ^{21}}{21}

= \frac{u ^{21}}{21}

Substitute back

u = x + 1

= \frac{( x + 1 ) ^{21}}{21}

Add a constant to the solution

= \frac{( x + 1 ) ^{21}}{21} + C

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What is the integral of (x^2+2x+1)^{10} ?
The integral of (x^2+2x+1)^{10} is ((x+1)^{21})/(21)+C