What is the integral of 7e^x-7xe^{x^2} ?

The integral of 7e^x-7xe^{x^2} is 7e^x-7/2 e^{x^2}+C

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integral of 7e^x-7xe^{x^2}

\int 7 e^{x} - 7 x e^{x^{2}} d x

7 e^{x} - \frac{7}{2} e^{x^{2}} + C

Solution steps

\int 7 e^{x} - 7 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 7 e^{x} d x - \int 7 x e^{x^{2}} d x

\int 7 e^{x} d x = 7 e^{x}

\int 7 x e^{x^{2}} d x = \frac{7}{2} e^{x^{2}}

= 7 e^{x} - \frac{7}{2} e^{x^{2}}

Add a constant to the solution

= 7 e^{x} - \frac{7}{2} e^{x^{2}} + C

What is the integral of 7e^x-7xe^{x^2} ?
The integral of 7e^x-7xe^{x^2} is 7e^x-7/2 e^{x^2}+C