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Question

Match the statements of Column I with values of Column II
Column IColumn II(A) e2x2exe2x+1dx=A ln(e2x+1)+B tan1(ex)+c(p) A=12, B=14(B) x+x2+2dx=A{x+x2+2}32+Bx+x2+2+c(q) A=12, B=2(C) cos 8xcos 7x1+2 cos 5xdx=A sin 3x+B sin 2x+c(r) A=13, B=2(D) ln xx3dx=Aln xx2+Bx2+c(s) A=13, B=12


A

A-s , B-r , C-q , D-p

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B

A-p , B-s , C-r , D-q

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C

A-p , B-q , C-r , D-s

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D

A-q , B-r , C-s , D-p

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Solution

The correct option is D

A-q , B-r , C-s , D-p


(A) e2xe2x+1dx2exe2x+1dx=12 ln(1+e2x)2 tan1(ex)+c

(B) x+x2+2=t
x2+2=t2+x22tx
x=12(t2t)
So, I=12t12(1+2t2)dt
I=12t12dt+t32dt=13t322t+c

(C) cos 8xcos 7x1+2 cos 5xdx
=2 sin 5x2 sin x2(32+2 cos 5x)dx1+2 cos 5x [sin 3(5x2)=3 sin 5x24 sin3 5x2]
=(cos 3xcos 2x)dx=sin 3x3sin 2x2+c

(D) ln xx3dx=(ln x)(12x2)+1x.12x2dx
=(12)ln xx2+(14)1x2+c


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