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Question

(3sinϕ2)cosϕ(5cos2ϕ4sinϕ)dϕ is
  1. 3ln(2sinϕ)4(sinϕ2)+c
  2. 3ln(sinϕ2)+42sinϕ+c
  3. ln(2sinϕ)+42sinϕ+c
  4. 3ln(2sinϕ)+4(2sinϕ)+c


Solution

The correct option is D 3ln(2sinϕ)+4(2sinϕ)+c
Let sinϕ=t,cosϕ dϕ=dt
I=(3t2)dt5(1t2)4t=3t2(t2)2
Let 3t2(t2)2=At2+B(t2)2
A=3,B=4
I=3t2dt+4(t2)2dtI=3ln(2sinϕ)+42sinϕ+c

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