What is the integral of (-3((9x^2)/2)-4x^3) ?

The integral of (-3((9x^2)/2)-4x^3) is -(9x^3)/2-x^4+C

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integral of (-3((9x^2)/2)-4x^3)

\int (- 3 (\frac{9 x ^{2}}{2}) - 4 x^{3}) d x

- \frac{9 x ^{3}}{2} - x^{4} + C

Solution steps

\int - 3 \cdot \frac{9 x ^{2}}{2} - 4 x^{3} 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

= - \int 3 \cdot \frac{9 x ^{2}}{2} d x - \int 4 x^{3} d x

\int 3 \cdot \frac{9 x ^{2}}{2} d x = \frac{9 x ^{3}}{2}

\int 4 x^{3} d x = x^{4}

= - \frac{9 x ^{3}}{2} - x^{4}

Add a constant to the solution

= - \frac{9 x ^{3}}{2} - x^{4} + C

What is the integral of (-3((9x^2)/2)-4x^3) ?
The integral of (-3((9x^2)/2)-4x^3) is -(9x^3)/2-x^4+C