# Integration by parts can you solve this problem please

• idir93
In summary, integration by parts is a method in calculus used to find the integral of a product of two functions. It involves breaking down a complex integral into two simpler integrals by using the product rule of differentiation. This method is most useful when the integral contains a product of two functions or when it is in the form of a product of an algebraic and a transcendental function. To solve an integral by parts, the steps are to identify the functions u and v, differentiate u and integrate v, substitute the values into the integration by parts formula, and simplify and solve for the integral. An example of solving an integral by parts is ∫xsin(x)dx = -½xsin(x) + ¼cos(x)x^
idir93
calculate : ∫x²e-x3dx by parts please i need details :) thank you very much

Last edited:

Don't use integration by parts! Let $u= x^3$.

Is it necessary to solve this using integration by parts? There's a nice substitution that makes the integral straightforward. I couldn't easily see a nice way to separate the integral.

i know that i can do it with u-substitution but I'm asked to integrate it by parts !

Then let u= 1/3, $dv= 3x^2e^{-x^3}$

i do not think that it's legal :) i mean that there is surely another method thank you anyway

## 1. What is integration by parts?

Integration by parts is a method in calculus used to find the integral of a product of two functions. It is based on the product rule of differentiation and is often used to evaluate integrals that cannot be solved using other methods.

## 2. How does integration by parts work?

Integration by parts involves breaking down a complex integral into two simpler integrals, using the product rule of differentiation. This allows us to rewrite the original integral in a different form that is easier to solve.

## 3. When should I use integration by parts?

Integration by parts is most useful when the integral contains a product of two functions, or when the integral is in the form of a product of an algebraic and a transcendental function.

## 4. What are the steps to solve an integral by parts?

The steps to solve an integral by parts are: 1) Identify the functions u and v, 2) Differentiate u and integrate v, 3) Substitute the values into the integration by parts formula, and 4) Simplify and solve for the integral.

## 5. Can you provide an example of solving an integral by parts?

Yes, for example, to solve the integral ∫xsin(x)dx, we would choose u = sin(x) and dv = xdx. Then, we would differentiate u to get du = cos(x)dx and integrate dv to get v = ½x^2. Substituting these values into the integration by parts formula, we get ∫xsin(x)dx = sin(x)½x^2 - ∫cos(x)½x^2dx. Simplifying and solving for the integral, we get ∫xsin(x)dx = -½xsin(x) + ¼cos(x)x^2 + C.

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