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Question

Integrate the following functions with respect to x:
i) sin2x+1x+1
ii) tan(3x+1)+e4x+5
iii) 2tan(4x+5)
iv) xx+2
v) sin2x

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Solution

(I) (sin2x+1x+1)dx
cos2x2+In(x+1)+c
(II) (tan(3x+1)+e4x+5)dx
=In|cos(3x+1)|3+e4x+54+c
(III) 2tan(4x+5)dx
=14×2In|cos(4x+5)|+c
(IV) xx+2dx=x+22x+2dx
=x+2dx2dxx72
(x+2)3/23/24x+2+c
(V) sin2x=1cos2xdx=xsin2x2+c
Hence putting in it with repultion.

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