- #1

idir93

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calculate : ∫x²e

^{-x3}dx by parts please i need details :) thank you very much
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- Thread starter idir93
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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^

- #1

idir93

- 21

- 0

calculate : ∫x²e^{-x3}dx by parts please i need details :) thank you very much

Last edited:

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- #2

HallsofIvy

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- #3

aeroplane

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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.

- #4

idir93

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

- #5

HallsofIvy

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

- #6

idir93

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

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.

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.

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.

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.

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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