Integration by Parts to find integral

Thread starter cummings15
Start date Dec 5, 2010
Tags

Integral Integration Integration by parts parts

In summary, integration by parts is a mathematical technique used to find the integral of a function by breaking it down into simpler parts. It is typically used when the integral involves a product of two functions, and one of the functions becomes simpler when differentiated. To apply integration by parts, one must use the formula: ∫ u dv = uv - ∫ v du, where u and v are functions and dv and du are the derivatives of those functions. The steps for using integration by parts are: 1. Identify u and dv in the integral. 2. Find the derivative of u and the antiderivative of dv. 3. Substitute these into the integration by parts formula. 4. Simplify and solve for the integral

Dec 5, 2010

cummings15

Homework Statement

find the integral of cot^(-1)of (5x)

Homework Equations

Integration by parts

The Attempt at a Solution

u = x
du = dx
dv = cot ^ (-1)
v = ?

and then i would plug into equation [uv- integral of vdu ]

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Dec 5, 2010

rock.freak667

Homework Helper

∫cot^-1(5x)dx

It would be more benefical to have u=cot^-1(5x) and dv=dx.

FAQ: Integration by Parts to find integral

What is integration by parts?

Integration by parts is a mathematical technique used to find the integral of a function by breaking it down into simpler parts.

When should I use integration by parts?

Integration by parts is typically used when the integral involves a product of two functions, and one of the functions becomes simpler when differentiated.

How do I apply integration by parts?

To apply integration by parts, you must use the formula: ∫ u dv = uv - ∫ v du, where u and v are functions and dv and du are the derivatives of those functions.

What are the steps for using integration by parts?

The steps for using integration by parts are:
1. Identify u and dv in the integral.
2. Find the derivative of u and the antiderivative of dv.
3. Substitute these into the integration by parts formula.
4. Simplify and solve for the integral.

Can integration by parts be used for definite integrals?

Yes, integration by parts can be used for definite integrals by applying the formula and then substituting the limits of integration into the final solution.