What is the integral of (2x+3)(x^2+3x)^5 ?

The integral of (2x+3)(x^2+3x)^5 is ((x^2+3x)^6)/6+C

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integral of (2x+3)(x^2+3x)^5

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

\frac{( x ^{2} + 3 x ) ^{6}}{6} + C

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

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

Substitute back

u = x^{2} + 3 x

= \frac{( x ^{2} + 3 x ) ^{6}}{6}

Add a constant to the solution

= \frac{( x ^{2} + 3 x ) ^{6}}{6} + C

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What is the integral of (2x+3)(x^2+3x)^5 ?
The integral of (2x+3)(x^2+3x)^5 is ((x^2+3x)^6)/6+C