What is the integral of 4x^2+5x-3 ?

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

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integral of 4x^2+5x-3

\int 4 x^{2} + 5 x - 3 d x

\frac{4 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x + C

Solution steps

\int 4 x^{2} + 5 x - 3 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 4 x^{2} d x + \int 5 x d x - \int 3 d x

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

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

\int 3 d x = 3 x

= \frac{4 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x + C

y = \frac{10}{1 + e ^{- x}}, (0, 5)

(3 x^{3} + 3) (x^{4} - 3 x)

\int_{0}^{5} x e^{- 4 x} d x

\int \frac{2}{9 - 4 x ^{2}} d x

\int_{1}^{3} \frac{1}{( x - 3 ) ^{2}} d x

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