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August 28, 2014

August 28, 2014

Posted by **Anonymous** on Sunday, November 18, 2007 at 12:02am.

Use Integration by parts to solve problems.

integral x^3(lnx)dx

u=lnx dv=x^3dx

du=1/x v=x^4/4

Answer:(x^3)(lnx)-(x^4/16)

integral xcosxdx

x cosx

1 sinx

0 -cosx

Answer: xcosx+cosx

integral e^2x(sinx)dx

u=e^2x dv=sinxdx

du=2e^2x v=-cosx

-e^x(cosx)+integral(2e^2x)(cosx)

Answer: I don't know. Help!

integral (x^2)(e^2x)

x^2 e^2x

2x (1/2)e^2x

2 (1/4)e^2x

0 (1/8)e^2x

Answer: (1/2)(x^2)(e^2x)-(1/2)(x)(e^2x)+(1/4)(e^2x)

- Calculus -
**drwls**, Sunday, November 18, 2007 at 12:20amintegral x^3(lnx)dx

u=lnx dv=x^3dx

du=1/x v=x^4/4

Answer:(x^4*lnx/4)-(x^4/16)

integral x cosxdx

u =x dv = cosxdx

du = 1 v = sin x

Answer: x sin x + cosx

Integral e^2x(sinx)dx

u=e^2x dv=sinxdx

du = 2e^2x v=-cosx

Answer -cos x*e^-2x +Integral 2 cos x e^2x

Now use the same integration by parts trick one more time to get a term that contains sin x e^2x on the right. Since you already have the same term on the left side, with a different coefficient, you can move all the sin x e^2x terms to one side of the equation and solve for it.

- Calculus -
**Anonymous**, Sunday, November 18, 2007 at 12:46pmCan you check if I did it correctly?

integral e^2x(sinx)dx

u=e^2x dv=sinxdx

du=2e^2x v=-cosx

-e^x(cosx)+integral(2e^2x)(cosx)

u=2e^2x dv=cosxdx

du=e^2x v=sinx

Answer: -e^2x(cosx)+(2e^2x)(sinx)-(e^x)(sinx)

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