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

The integral of (xe^{-x^2}+(e^x)/(e^x+3)) is -1/2 e^{-x^2}+ln|e^x+3|+C

Popular >

integral of (xe^{-x^2}+(e^x)/(e^x+3))

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

- \frac{1}{2} e^{- x^{2}} + ln ∣ e^{x} + 3 ∣ + C

Solution steps

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

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

\int \frac{e ^{x}}{e ^{x} + 3} d x = ln ∣ e^{x} + 3 ∣

= - \frac{1}{2} e^{- x^{2}} + ln ∣ e^{x} + 3 ∣

Add a constant to the solution

= - \frac{1}{2} e^{- x^{2}} + ln ∣ e^{x} + 3 ∣ + C

\int_{- 2}^{3} \frac{15}{x ^{4}} d x

\frac{d y}{d x} = - (3 - y)^{2}

x^{2} \frac{d y}{d x} = y - y x

\frac{\partial}{\partial y} (y cos (x y))

x \to \infty lim (\frac{14}{x})

What is the integral of (xe^{-x^2}+(e^x)/(e^x+3)) ?
The integral of (xe^{-x^2}+(e^x)/(e^x+3)) is -1/2 e^{-x^2}+ln|e^x+3|+C