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What is the Antiderivitive of xsin(7x)?

Guest Oct 15, 2014

Best Answer 

 #1
avatar+17744 
+5

Do you have integration by parts?

If so:  ∫u dv  =  u·v -∫v du

Let u = x  -->  du = dx

Let dv = sin(7x)dx  -->  v = -(1/7)cos(7x) 

Substituting:  ∫xsin(7x)dx  =  -(x/7)cos(7x) - ∫-(1/7)cos(7x)dx

                     ∫xsin(7x)dx  =  -(x/7)cos(7x) +(1/7) ∫cos(7x)dx

                     ∫xsin(7x)dx  =  -(x/7)cos(7x) + (1/49)sin(7x) + C

geno3141  Oct 15, 2014
 #1
avatar+17744 
+5
Best Answer

Do you have integration by parts?

If so:  ∫u dv  =  u·v -∫v du

Let u = x  -->  du = dx

Let dv = sin(7x)dx  -->  v = -(1/7)cos(7x) 

Substituting:  ∫xsin(7x)dx  =  -(x/7)cos(7x) - ∫-(1/7)cos(7x)dx

                     ∫xsin(7x)dx  =  -(x/7)cos(7x) +(1/7) ∫cos(7x)dx

                     ∫xsin(7x)dx  =  -(x/7)cos(7x) + (1/49)sin(7x) + C

geno3141  Oct 15, 2014
 #2
avatar+92781 
0

Thanks Gino  

Melody  Oct 16, 2014

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