What is the integral of (5x^2+3x-10) ?

The integral of (5x^2+3x-10) is (5x^3)/3+(3x^2)/2-10x+C

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integral of (5x^2+3x-10)

\int (5 x^{2} + 3 x - 10) d x

\frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x + C

Solution steps

\int 5 x^{2} + 3 x - 10 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 5 x^{2} d x + \int 3 x d x - \int 10 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 10 d x = 10 x

= \frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x

Add a constant to the solution

= \frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x + C

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y \to 15 lim (y + 3)

\int \frac{sin ( 2 e ^{- 4 x} )}{e ^{4 x}} d x

f (x) = x^{3} - 3 x^{2} + 3 x, g (x) = x

What is the integral of (5x^2+3x-10) ?
The integral of (5x^2+3x-10) is (5x^3)/3+(3x^2)/2-10x+C