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whatlifeforme
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Homework Statement
integrate by parts.
Integral: x * 5^x
Homework Equations
The Attempt at a Solution
i got to (1/ln5) * 5^x ;; and I'm not sure how to integrate further.
How about giving a few details regarding how you got that answer & where you are in the process of integration by parts.whatlifeforme said:Homework Statement
integrate by parts.
Integral: x * 5^x
Homework Equations
The Attempt at a Solution
i got to (1/ln5) * 5^x ;; and I'm not sure how to integrate further.
whatlifeforme said:so would the final simplified answer be:
(x/ln5)(5^x) - (5^x/(ln(5)^2)
Integration by parts is a technique used in calculus to find the integral of a product of two functions. It involves using the product rule for differentiation, but in reverse.
To use integration by parts for x * 5^x, you would first identify which function is the "u" function and which is the "dv" function. In this case, "u" would be x and "dv" would be 5^x. Then, use the formula: ∫ u dv = uv - ∫ v du to solve for the integral.
The formula for integration by parts is: ∫ u dv = uv - ∫ v du, where "u" and "v" are functions and "du" and "dv" are their respective differentials.
Yes, integration by parts can be used for a wide range of functions, including logarithmic, exponential, trigonometric, and polynomial functions.
Integration by parts is useful because it provides an alternate method for solving integrals that may be difficult or impossible to solve using other techniques. It is also helpful in simplifying complex integrals and finding solutions to problems in physics and engineering.