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

The integral of 3x^4(2x-5) is 3(2/5 x^6-x^5-(x^6)/(15))+C

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

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

3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{4} (2 x - 5) d x

Apply Integration By Parts

= 3 (\frac{1}{5} x^{5} (2 x - 5) - \int \frac{2 x ^{5}}{5} d x)

\int \frac{2 x ^{5}}{5} d x = \frac{x ^{6}}{15}

= 3 (\frac{1}{5} x^{5} (2 x - 5) - \frac{x ^{6}}{15})

Expand

\frac{1}{5} x^{5} (2 x - 5) : \frac{2}{5} x^{6} - x^{5}

= 3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15})

Add a constant to the solution

= 3 (\frac{2}{5} x^{6} - x^{5} - \frac{x ^{6}}{15}) + C

What is the integral of 3x^4(2x-5) ?
The integral of 3x^4(2x-5) is 3(2/5 x^6-x^5-(x^6)/(15))+C