What is the integral of (ex^2+pi) ?

The integral of (ex^2+pi) is (ex^3)/3+pix+C

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integral of (ex^2+pi)

\int (e x^{2} + π) d x

\frac{e x ^{3}}{3} + π x + C

Solution steps

\int e x^{2} + π 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 e x^{2} d x + \int π d x

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

\int π d x = π x

= \frac{e x ^{3}}{3} + π x

Add a constant to the solution

= \frac{e x ^{3}}{3} + π x + C

x \to 0 lim (\frac{( 2 ∣ x ∣ )}{3 x})

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