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# What is the Antiderivitive of xsin(7x)?

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What is the Antiderivitive of xsin(7x)?

Guest Oct 15, 2014

#1
+17721
+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
Sort:

#1
+17721
+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
#2
+92217
0

Thanks Gino

Melody  Oct 16, 2014

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