What is the integral of 8x^2+3x-5 ?

The integral of 8x^2+3x-5 is (8x^3)/3+(3x^2)/2-5x+C

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integral of 8x^2+3x-5

\int 8 x^{2} + 3 x - 5 d x

\frac{8 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 5 x + C

Solution steps

\int 8 x^{2} + 3 x - 5 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 8 x^{2} d x + \int 3 x d x - \int 5 d x

\int 8 x^{2} d x = \frac{8 x ^{3}}{3}

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

\int 5 d x = 5 x

= \frac{8 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 5 x

Add a constant to the solution

= \frac{8 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 5 x + C

y^{^{'}} = 4 x + y, y (0) = 5

y = - 3 x^{2}, (- 4, - 48)

\int_{0}^{1} t e^{t} d t

\int_{9}^{10} - 6 d x

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

What is the integral of 8x^2+3x-5 ?
The integral of 8x^2+3x-5 is (8x^3)/3+(3x^2)/2-5x+C