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

The integral of x^3(x^4+3) is 1/4 x^4(x^4+3)-(x^8)/8+C

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integral of x^3(x^4+3)

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

\frac{1}{4} x^{4} (x^{4} + 3) - \frac{x ^{8}}{8} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{4} x^{4} (x^{4} + 3) - \int x^{7} d x

= \frac{1}{4} x^{4} (x^{4} + 3) - \int x^{7} d x

\int x^{7} d x = \frac{x ^{8}}{8}

= \frac{1}{4} x^{4} (x^{4} + 3) - \frac{x ^{8}}{8}

Add a constant to the solution

= \frac{1}{4} x^{4} (x^{4} + 3) - \frac{x ^{8}}{8} + C

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What is the integral of x^3(x^4+3) ?
The integral of x^3(x^4+3) is 1/4 x^4(x^4+3)-(x^8)/8+C