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Question

The integral sec2x(secx+tanx)9/2dx equals (for some arbitrary constant k)


A
1(secx+tanx)112{11117(secx+tanx)2}+k
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B
1(secx+tanx)112{11117(secx+tanx)2}+k
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C
1(secx+tanx)112{111+17(secx+tanx)2}+k
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D
1(secx+tanx)112{111+17(secx+tanx)2}+k
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Solution

The correct option is C 1(secx+tanx)112{111+17(secx+tanx)2}+k

Put secx+tanx=t
secx(secx+tanx)dx=dt
secxdx=dtt
and secxtanx=1t
secx=t+1t2
secxt.t9/2dt=12(t+1t)t.t9/2dt
=12(1t9/2+1t13/2)dt
=12[27t7/2+111t11/2]+k
=1t11/2[t27+111]+k

=1(secx+tanx)112{111+17(secx+tanx)2}+k


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