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

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

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integral of 4x^2+3x+5

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

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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