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Question:

The integral ∫(1+x⁻¹ )ex+1/xdx is equal to

(x⁻¹)ex+1/x+c

xex+1/x+c

-xex+1/x+c

(x+1)ex+1/x+c

Solution:

∫(1+x⁻¹ )ex+1/xdx=∫e(x+1/x)dx+∫x(1/x²)e(x+1/x)dx=∫e(x+1/x)dx+xe(x+1/x)-∫e(x+1/x)dx
Using integration by parts
=xe(x+1/x)+c