What is the integral of (x^3+2x)^{25}(3x^2+2) ?

The integral of (x^3+2x)^{25}(3x^2+2) is ((x^3+2x)^{26})/(26)+C

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integral of (x^3+2x)^{25}(3x^2+2)

\int (x^{3} + 2 x)^{25} (3 x^{2} + 2) d x

\frac{( x ^{3} + 2 x ) ^{26}}{26} + C

Solution steps

\int (x^{3} + 2 x)^{25} (3 x^{2} + 2) d x

Apply u-substitution

: \int u^{25} d u

= \int u^{25} d u

Apply the Power Rule

: \frac{u ^{26}}{26}

= \frac{u ^{26}}{26}

Substitute back

u = x^{3} + 2 x

= \frac{( x ^{3} + 2 x ) ^{26}}{26}

Add a constant to the solution

= \frac{( x ^{3} + 2 x ) ^{26}}{26} + C

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What is the integral of (x^3+2x)^{25}(3x^2+2) ?
The integral of (x^3+2x)^{25}(3x^2+2) is ((x^3+2x)^{26})/(26)+C