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Calculus/cal 2
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Question
hi
i've some questions regarding cal 2
how can integrate the following?
1- e^(x^2)*x^3 dx
2- e^(2x)*sin(3x) dx
i think i should use integration by parts
but how
your help is very appreciated
1. Integration by parts.
Let u = x² and dv = x(e^x²).
This gives u = 2x and dv = e^x²/2.
2. Integration by parts. Twice.
Use u=e^(2x) and dv = sin(3x).
On the results, there will be another integral with e^(2x) and cos(3x) in it and some constants.
Let u = e^(2x) and dv = cos(3x) and do that integral.
The result should have another integral of e^(2x)sin(3x) in it, but this time with a contant.
Take the start of this problem and the end and note that they are equal.
Subtract the integral that is on the right from both sids. This will give you all of the integral on the left times some constant and a function on the right. Divide by the constant and there is the value of the integral.
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