thegoosegirl42 said:Homework Statement
Evaluate the integral of (x+1)5^(x+1)^2
Homework Equations
The Attempt at a Solution
I set my u=(x+1) making du=1dx. This makes it u*5^u^2. I integrated the first u to be ((x+1)^2/2) however I don't know what to do with the 5^u^2
U substitution is a technique used in integration to replace a complex expression with a simpler one in order to make the integration process easier. It is typically used when an integral contains a function within another function, such as a polynomial within a trigonometric function.
The substitution for u is typically chosen based on the expression within the integral. It should be a function that when differentiated, will result in some or all of the terms in the original integral. Common choices for u include trigonometric functions, exponential functions, and polynomials.
To perform u substitution, follow these steps:
No, u substitution is most effective when the integral contains a function within another function. It may not be useful for integrals with complicated expressions or those that require other integration techniques, such as integration by parts.
If the integral after the substitution is simpler or easier to integrate than the original, then the substitution was successful. It should also result in an answer that matches the original integral when u is replaced with the original function.