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

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

\int x^{2} + x + 6 d x

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

x^{2} y^{^{''}} - 3 x y^{^{'}} + 4 y = x, y (1) = 0, y^{^{'}} (1) = 0

n = 1 \sum \infty n! (2 x - 1)^{n}

\frac{d x}{d t} = - 8

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