What is the integral of (x^2+2x)^5(2x+2) ?

The integral of (x^2+2x)^5(2x+2) is ((x^2+2x)^6)/6+C

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integral of (x^2+2x)^5(2x+2)

\int (x^{2} + 2 x)^{5} (2 x + 2) d x

\frac{( x ^{2} + 2 x ) ^{6}}{6} + C

Solution steps

\int (x^{2} + 2 x)^{5} (2 x + 2) d x

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = x^{2} + 2 x

= \frac{( x ^{2} + 2 x ) ^{6}}{6}

Add a constant to the solution

= \frac{( x ^{2} + 2 x ) ^{6}}{6} + C

\frac{d}{d x} (x^{5} e^{- x})

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

\int_{0}^{3} x 16 - x^{2} d x

x \to 0 lim (- x ln (x) - x)

\int x \cdot x d x

What is the integral of (x^2+2x)^5(2x+2) ?
The integral of (x^2+2x)^5(2x+2) is ((x^2+2x)^6)/6+C