What is the integral of (x^4+3x)^{30}(4x^3+3) ?

The integral of (x^4+3x)^{30}(4x^3+3) is ((x^4+3x)^{31})/(31)+C

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integral of (x^4+3x)^{30}(4x^3+3)

\int (x^{4} + 3 x)^{30} (4 x^{3} + 3) d x

\frac{( x ^{4} + 3 x ) ^{31}}{31} + C

Solution steps

\int (x^{4} + 3 x)^{30} (4 x^{3} + 3) d x

Apply u-substitution

: \int u^{30} d u

= \int u^{30} d u

Apply the Power Rule

: \frac{u ^{31}}{31}

= \frac{u ^{31}}{31}

Substitute back

u = x^{4} + 3 x

= \frac{( x ^{4} + 3 x ) ^{31}}{31}

Add a constant to the solution

= \frac{( x ^{4} + 3 x ) ^{31}}{31} + C

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What is the integral of (x^4+3x)^{30}(4x^3+3) ?
The integral of (x^4+3x)^{30}(4x^3+3) is ((x^4+3x)^{31})/(31)+C