Integrate S x^2(e^((x^3)+1)) with Parts - Step-by-Step

Thread starter satxer
Start date May 8, 2010
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Indefinite Indefinite integral Integral

In summary, integration by parts is a technique used in calculus to solve integrals that are in the form of a product. It involves breaking down the integral into two parts and using the product rule to solve it. The choice of which part to differentiate and which to integrate is usually based on the LIATE rule. The formula for integration by parts is ∫u dv = uv - ∫v du, and it can be applied to solve integrals by following a step-by-step process. To integrate S x^2(e^((x^3)+1)) with parts, one would first let u = x^2 and dv = e^((x^3)+1) dx, find du and v, and then apply the

May 8, 2010

satxer

S x^2(e^((x^3)+1))

I know I have to use integration by parts, and I'm guessing I should find the derivative of e^((x^3)+1), but I really have no idea where to start...

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May 8, 2010

Dick

Science Advisor

Homework Helper

You don't have to do an integration by parts. It's a simple u substitution. You should always try that first.

May 8, 2010

lanedance

Homework Helper

do you have to use parts? how about just a substitution?

FAQ: Integrate S x^2(e^((x^3)+1)) with Parts - Step-by-Step

What is integration by parts?

Integration by parts is a technique used in calculus to solve integrals that are in the form of a product. It involves breaking down the integral into two parts and using the product rule to solve it.

How do you determine which part of the integral to differentiate and which to integrate?

In integration by parts, one part of the integral is chosen to be differentiated and the other to be integrated. This choice is usually made based on the LIATE rule, which stands for Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential functions. The function that is higher on this list is chosen to be differentiated.

What is the formula for integration by parts?

The formula for integration by parts is ∫u dv = uv - ∫v du, where u and v are the parts of the integral that are differentiated and integrated, respectively.

How do you apply integration by parts to solve the given integral?

To apply integration by parts to solve the given integral, you need to follow these steps:

Choose which part of the integral to differentiate and which to integrate.
Apply the formula ∫u dv = uv - ∫v du.
Simplify the integral by using algebraic manipulations.
Repeat the process until the integral is in a form that can be easily solved.
Finally, solve the integral and include the constant of integration if necessary.

What is the step-by-step process for integrating S x^2(e^((x^3)+1)) with parts?

The step-by-step process for integrating S x^2(e^((x^3)+1)) with parts is as follows:

Let u = x^2 and dv = e^((x^3)+1) dx.
Find du and v by differentiating and integrating u and dv, respectively.
Apply the formula ∫u dv = uv - ∫v du to the given integral.
Simplify the integral by using algebraic manipulations.
Repeat the process until the integral is in a form that can be easily solved.
Finally, solve the integral and include the constant of integration if necessary.