# Andy_Nguyen_Week 7 Lab - MATRH260Week 7 Lab Name Andy...

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MATRH260—Week 7 LabName:Andy NguyenLogarithmic IntegralsExamine each example below then answer questions 1–3.Integral: 1xdxIntegral:1x3dxSolution: ln |x| +CSolution: ln|x+3|+CIntegral:2xx2+4dxIntegral:12x3dxSolution: ln|x2+4|+CSolution: 12ln|2x3|+C1) What is the formula for finding duu?Du/u=ln |u| + c2) How is substitution being used to solve examples and ? Show u and du.U=x2+4Du=2x dxU=2x-3Du=2 dx3) Why can’t we find the integral 1xdxusing the following set-up? 1xdx=x1dxBecause the Integral is being converted to the inverse of the solution, which means the Integral of 1/xdx cannot be found.
4) Fill in the blanks below with the correct information for the following integral: 34x+5dxu =4x+5du =3Substitution =12/9dxIntegration =1/7x+5Final answer =3ln|4x+5|/4+C . C being used as the arbitrary constant.u =X^3-5du =E^3x^2Substitution =9x^2Integration =9ex^3/4-5Final answer =The final answer would be the same as the starting integral.u =E^3x^2-ddu =6xe^3x^2Substitution =20ex/5eIntegration =18xe^2/1Final answer =Ln|e^3x^2-5|+C
Exponential IntegralsExamine each example below and answer questions 7–10.