Solve by not using partial fractions. I liked this particular integral, I solved it on another forum to show that sometimes we can avoid the annoying algebra when doing the partial fractions.
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Sub. on the third integral , we have For the second integral , use integration by parts , Therefore ,
I observe that: So we have: Where for the last integral we use the substitution to get: Letting in the remaining integral we have: Thus
good! pretty different solutions from the one i have: consider (1); now from put and the integral becomes (2). on the original integral put then from (1) and (2) the latter equals and the original integral equals
What about letting right away. The integral becomes or or Integrating gives Then backsubstitute noting that
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