Integration by parts (i think)

[PhysicsMajor]

Greetings all,

here goes...

The integral of (xe^(x))/((x+1)^(2))

Thanks

 

[whozum]

$$\int{\frac{xe^x}{(x+1)^2}}{dx}$$

$$u = \frac{-1}{x+1}$$

$$du = \frac{1}{(x+1)^2}$$

$$v = xe^x$$

$$dv = e^x(x+1)$$

$$\int{v}{du} = uv - \int{u}{dv}$$

$$\int{\frac{xe^x}{(x+1)^2}}{dx} = \frac{-xe^x}{x+1} + \int{e^x}{dx}$$

Hope that helps you out. Not a very hard problem from there ;)

 

[M98Ranger]

for sharing your thoughts on integration by parts. You are correct, this integral can be solved using integration by parts. This method is often used to solve integrals that involve products of functions. In this case, we can choose u = x and dv = (e^x)/((x+1)^2)dx. Then, using the integration by parts formula, we get:

∫(xe^x)/((x+1)^2)dx = xe^x/(x+1) - ∫e^x/(x+1)dx

We can solve the remaining integral using partial fractions or by using the substitution method. Either way, we will eventually arrive at the solution for the original integral. Integration by parts is a useful tool in calculus and can be used in various situations to solve integrals. Thank you for bringing up this integral for discussion.