What is the integral of (x^3+x^2)^{12}(3x^2+2x) ?

The integral of (x^3+x^2)^{12}(3x^2+2x) is ((x^3+x^2)^{13})/(13)+C

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integral of (x^3+x^2)^{12}(3x^2+2x)

\int (x^{3} + x^{2})^{12} (3 x^{2} + 2 x) d x

\frac{( x ^{3} + x ^{2} ) ^{13}}{13} + C

Solution steps

\int (x^{3} + x^{2})^{12} (3 x^{2} + 2 x) d x

Apply u-substitution

: \int u^{12} d u

= \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= \frac{u ^{13}}{13}

Substitute back

u = x^{3} + x^{2}

= \frac{( x ^{3} + x ^{2} ) ^{13}}{13}

Add a constant to the solution

= \frac{( x ^{3} + x ^{2} ) ^{13}}{13} + C

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What is the integral of (x^3+x^2)^{12}(3x^2+2x) ?
The integral of (x^3+x^2)^{12}(3x^2+2x) is ((x^3+x^2)^{13})/(13)+C