What is the integral of (5+e^{3x^2})x ?

The integral of (5+e^{3x^2})x is (5x^2)/2+1/6 e^{3x^2}+C

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integral of (5+e^{3x^2})x

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

\frac{5 x ^{2}}{2} + \frac{1}{6} e^{3 x^{2}} + C

Solution steps

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

Expand

(5 + e^{3 x^{2}}) x : 5 x + e^{3 x^{2}} x

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

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

\int e^{3 x^{2}} x d x = \frac{1}{6} e^{3 x^{2}}

= \frac{5 x ^{2}}{2} + \frac{1}{6} e^{3 x^{2}}

Add a constant to the solution

= \frac{5 x ^{2}}{2} + \frac{1}{6} e^{3 x^{2}} + C

What is the integral of (5+e^{3x^2})x ?
The integral of (5+e^{3x^2})x is (5x^2)/2+1/6 e^{3x^2}+C