What is the integral of (2+5x^4)x^3 ?

The integral of (2+5x^4)x^3 is 1/4 x^4(2+5x^4)-(5x^8)/8+C

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integral of (2+5x^4)x^3

\int (2 + 5 x^{4}) x^{3} d x

\frac{1}{4} x^{4} (2 + 5 x^{4}) - \frac{5 x ^{8}}{8} + C

Solution steps

\int (2 + 5 x^{4}) x^{3} d x

Apply Integration By Parts

: \frac{1}{4} x^{4} (2 + 5 x^{4}) - \int 5 x^{7} d x

= \frac{1}{4} x^{4} (2 + 5 x^{4}) - \int 5 x^{7} d x

\int 5 x^{7} d x = \frac{5 x ^{8}}{8}

= \frac{1}{4} x^{4} (2 + 5 x^{4}) - \frac{5 x ^{8}}{8}

Add a constant to the solution

= \frac{1}{4} x^{4} (2 + 5 x^{4}) - \frac{5 x ^{8}}{8} + C

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What is the integral of (2+5x^4)x^3 ?
The integral of (2+5x^4)x^3 is 1/4 x^4(2+5x^4)-(5x^8)/8+C