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Question

If f(x)dx=ψ(x), then x5f(x3)dx is equal to

A
13[x3ψ(x3)x2ψ(x3)dx]+c
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B
13x3ψ(x3)3x3ψ(x3)dx+c
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C
13x3ψ(x3)x2ψ(x3)dx+c
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D
13[x3ψ(x3)x3ψ(x3)dx]+c
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Solution

The correct option is C 13x3ψ(x3)x2ψ(x3)dx+c
Given f(x)dx=ψ(x)Let I=x5f(x3)dxPut x3=t3x2dx=dtI=133.x2.x3.f(x3).dx=13tf(t)dt=13[tf(t)dt(ddt(t)f(t)dt)dt]=13[tψ(t)ψ(t)dt]=13[x3ψ(x3)3x2ψ(x3)dx+c]=13x3ψ(x3)x2ψ(x3)dx+c

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