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B
13x3ψ(x3)−3∫x3ψ(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 C13x3ψ(x3)−∫x2ψ(x3)dx+c Given ∫f(x)dx=ψ(x)Let I=∫x5f(x3)dxPut x3=t⇒3x2dx=dtI=13∫3.x2.x3.f(x3).dx=13∫tf(t)dt=13[t∫f(t)dt−∫(ddt(t)∫f(t)dt)dt]=13[tψ(t)−∫ψ(t)dt]=13[x3ψ(x3)−3∫x2ψ(x3)dx+c]=13x3ψ(x3)−∫x2ψ(x3)dx+c