Using u-sub for inetgral(x^4sinxdx)

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In summary, u-substitution is a technique used in integration to simplify and solve complex integrals by substituting a variable with a new variable u. It is typically used when the integrand contains a product of two functions, one of which is the derivative of the other. The general process involves identifying the u-value to substitute, finding its derivative, and then substituting it into the integral. It can also be used to solve integrals involving trigonometric, exponential, and radical functions, but may not always be the most efficient method.
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aglo6509
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So I came across a problem that said to use u-sub to solve:

integral(x^4sinxdx)

But the only way I could think of solving it is by the tabular method (or by parts.) I'm not asking in the sense of a homework question I'm just curious to see what I substitute u for in this problem.

Thanks.
 
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hi aglo6509! :smile:

(try using the X2 button just above the Reply box :wink:)

i don't think you can solve that by a substitution :redface:
 

What is u-substitution?

U-substitution is a technique used in integration to simplify and solve complex integrals. It involves substituting a variable with a new variable u, which helps to transform the integral into a simpler form.

How do I know when to use u-substitution?

U-substitution is typically used when the integrand contains a product of two functions, one of which is the derivative of the other. This is known as the chain rule in differentiation, and the inverse process is used in integration.

What is the general process for using u-substitution?

The general process for u-substitution involves identifying the u-value to substitute, finding its derivative, and then substituting it into the integral. This will often result in an easier integral to solve, which can then be integrated using basic rules.

How is u-substitution used to solve the integral of x^4sin(x)dx?

In this case, we can let u = x^2, which means du = 2x dx. Substituting these values into the integral, we get 1/2∫sin(u)du. This can be integrated using the basic rule for the integral of sin(x), giving us the final answer of -1/2cos(x^2) + C.

Can u-substitution be used for other types of integrals?

Yes, u-substitution can be used for a variety of integrals. It is especially useful for integrals that involve trigonometric functions, exponential functions, and radical functions. However, it may not always be the most efficient or effective method for solving integrals, so it is important to consider other techniques as well.

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