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Question

sinx+cosx9+16sin2xdx

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Solution

Let sinxcosx=t
(cosx+sinx)dx=dt (sinxcosx)2=t2
Squaring on both sides
sin2x+cos2x2sinxcosx=t2
1sin2x=t2
sin2x=1t2
sinx+cosx9+16sin2xdx
dt9+16sin2x=dt2516t2=116dt(54)216t2
=116×12(54)log∣ ∣ ∣ ∣54+t54t∣ ∣ ∣ ∣+c =140log5+4(sinxcosx)54(sinxcosx)+c


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