What is the integral of-15x^4(-3x^5-1) ?

The integral of-15x^4(-3x^5-1) is -15(-(3x^{10}}{10}-\frac{x^5)/5)+C

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integral of-15x^4(-3x^5-1)

\int - 15 x^{4} (- 3 x^{5} - 1) d x

- 15 (- \frac{3 x ^{10}}{10} - \frac{x ^{5}}{5}) + C

Solution steps

\int - 15 x^{4} (- 3 x^{5} - 1) d x

Take the constant out:

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

= - 15 \cdot \int x^{4} (- 3 x^{5} - 1) d x

Expand

x^{4} (- 3 x^{5} - 1) : - 3 x^{9} - x^{4}

= - 15 \cdot \int - 3 x^{9} - x^{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - 15 (- \int 3 x^{9} d x - \int x^{4} d x)

\int 3 x^{9} d x = \frac{3 x ^{10}}{10}

\int x^{4} d x = \frac{x ^{5}}{5}

= - 15 (- \frac{3 x ^{10}}{10} - \frac{x ^{5}}{5})

Add a constant to the solution

= - 15 (- \frac{3 x ^{10}}{10} - \frac{x ^{5}}{5}) + C

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What is the integral of-15x^4(-3x^5-1) ?
The integral of-15x^4(-3x^5-1) is -15(-(3x^{10}}{10}-\frac{x^5)/5)+C