What is the integral of 30(25-x^2) ?

The integral of 30(25-x^2) is 30(25x-(x^3)/3)+C

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integral of 30(25-x^2)

\int 30 (25 - x^{2}) d x

30 (25 x - \frac{x ^{3}}{3}) + C

Solution steps

\int 30 (25 - x^{2}) d x

Take the constant out:

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

= 30 \cdot \int 25 - 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

= 30 (\int 25 d x - \int x^{2} d x)

\int 25 d x = 25 x

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

= 30 (25 x - \frac{x ^{3}}{3})

Add a constant to the solution

= 30 (25 x - \frac{x ^{3}}{3}) + C

f (x) = 7 ln (x), at x = 3

\frac{d}{d x} (a e^{x})

f (x) = (2 x + 1) (3 x - 2)

\int_{3}^{e^{4}} \frac{1}{x} d x

y = ln (x), y = 0, x = e

What is the integral of 30(25-x^2) ?
The integral of 30(25-x^2) is 30(25x-(x^3)/3)+C