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

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

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integral of 3x^2+4x+5

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

x^{3} + 2 x^{2} + 5 x + C

Solution steps

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

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

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

\int 5 d x = 5 x

= x^{3} + 2 x^{2} + 5 x

Add a constant to the solution

= x^{3} + 2 x^{2} + 5 x + C

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

\int \frac{1}{1 + \frac{x}{2 L}} d x

\int x^{2} e^{2 x^{3} + 1} d x

\int (x + 5) 2 - x d x

\int 2 x - 2 x^{3} d x