What is the integral of 3e^x-3xe^{x^2} ?

The integral of 3e^x-3xe^{x^2} is 3e^x-3/2 e^{x^2}+C

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integral of 3e^x-3xe^{x^2}

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

3 e^{x} - \frac{3}{2} e^{x^{2}} + C

Solution steps

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

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

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

= 3 e^{x} - \frac{3}{2} e^{x^{2}}

Add a constant to the solution

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

\frac{d}{d x} (k x + d)

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

\int \frac{1}{2 x ^{3} - 3 x ^{2}} d x

x^{2} (3 - x)

What is the integral of 3e^x-3xe^{x^2} ?
The integral of 3e^x-3xe^{x^2} is 3e^x-3/2 e^{x^2}+C