Well, there will be several ones. It were really helpful if someone could also explain some details; 1) I (x^3-x^2-3x+1)/(x^2+x-2)dx 2) I sin4x*sin5x dx 3) I e^cosx sinx dx 4) I x artctgx dx 5) I (1/x^2)*e^1/x dx
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Hello, lightbird! Here are a few of them . . . Long division: . Let Substitute: . Let Substitute: .
Originally Posted by lightbird Well, there will be several ones. It were really helpful if someone could also explain some details; 1) I (x^3-x^2-3x+1)/(x^2+x-2)dx 2) I sin4x*sin5x dx 3) I e^cosx sinx dx 4) I x artctgx dx 5) I (1/x^2)*e^1/x dx 1) Divide the quadratic into the cubic and apply partial fraction decomposition to the remainder to get . Now integrate term-by-term. 2) Apply the identity . In your case A = 4x and B = 5x. 3) Make the substitution . 4) Integration by parts. 5) Make the substitution .
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