What is the integral of x^2(5^3+7^2-6x-3) ?

The integral of x^2(5^3+7^2-6x-3) is -(3x^4)/2+57x^3+C

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integral of x^2(5^3+7^2-6x-3)

\int x^{2} (5^{3} + 7^{2} - 6 x - 3) d x

- \frac{3 x ^{4}}{2} + 57 x^{3} + C

Solution steps

\int x^{2} (5^{3} + 7^{2} - 6 x - 3) d x

Simplify

= \int x^{2} (- 6 x + 171) d x

Expand

x^{2} (- 6 x + 171) : - 6 x^{3} + 171 x^{2}

= \int - 6 x^{3} + 171 x^{2} 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 6 x^{3} d x + \int 171 x^{2} d x

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 171 x^{2} d x = 57 x^{3}

= - \frac{3 x ^{4}}{2} + 57 x^{3}

Add a constant to the solution

= - \frac{3 x ^{4}}{2} + 57 x^{3} + C

x = - 2, x = 1, y = e^{x}, y = 3 - e^{x}

\int (cot (x)) [ln (sin (x))] d x

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(x + 2 y^{2}) d x + x y d y = 0

What is the integral of x^2(5^3+7^2-6x-3) ?
The integral of x^2(5^3+7^2-6x-3) is -(3x^4)/2+57x^3+C