What is the integral of (u^2+3-ue^{7-u^2}) ?

The integral of (u^2+3-ue^{7-u^2}) is (u^3)/3+3u+1/2 e^{7-u^2}+C

integral of (u^2+3-ue^{7-u^2})

\int (u^{2} + 3 - u e^{7 - u^{2}}) d u

\frac{u ^{3}}{3} + 3 u + \frac{1}{2} e^{7 - u^{2}} + C

Solution steps

\int u^{2} + 3 - u e^{7 - u^{2}} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{2} d u + \int 3 d u - \int u e^{7 - u^{2}} d u

\int u^{2} d u = \frac{u ^{3}}{3}

\int 3 d u = 3 u

\int u e^{7 - u^{2}} d u = - \frac{1}{2} e^{7 - u^{2}}

= \frac{u ^{3}}{3} + 3 u - (- \frac{1}{2} e^{7 - u^{2}})

Simplify

= \frac{u ^{3}}{3} + 3 u + \frac{1}{2} e^{7 - u^{2}}

Add a constant to the solution

= \frac{u ^{3}}{3} + 3 u + \frac{1}{2} e^{7 - u^{2}} + C

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What is the integral of (u^2+3-ue^{7-u^2}) ?
The integral of (u^2+3-ue^{7-u^2}) is (u^3)/3+3u+1/2 e^{7-u^2}+C