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x-2-1-x-1-2-e-x-dx-




Question Number 69715 by Mikaell last updated on 26/Sep/19
∫((x^2 +1)/((x+1)^2 ))e^x dx
x2+1(x+1)2exdx
Answered by mind is power last updated on 27/Sep/19
∫((x^2 +1)/(x^2 +2x+1))e^x dx=∫((x^2 +2x+1−2x)/((x^2 +2x+1)))=∫e^x dx−∫((2x)/(x^2 +2x+1))e^x dx  ∫e^x dx−2∫(((x+1)e^x −e^x )/((x+1)^2 ))dx=∫e^x dx−2∫(((x+1)(e^x )′−(x+1)′e^x )/((x+1)^2 ))∫e^x dx−2∫d((e^x /(x+1)))  =e^x −2(e^x /(x+1))+c=(((x−1)e^x )/(x+1))+c
x2+1x2+2x+1exdx=x2+2x+12x(x2+2x+1)=exdx2xx2+2x+1exdxexdx2(x+1)exex(x+1)2dx=exdx2(x+1)(ex)(x+1)ex(x+1)2exdx2d(exx+1)=ex2exx+1+c=(x1)exx+1+c
Commented by Mikaell last updated on 27/Sep/19
thank you Sir
thankyouSir

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