Showing all your working, evaluate ∫(21x^6 - e^2x- (1/x) +6)dx

 ∫(21x⁶-e^2x-1/x+6)dx

To tackle this question, I would do each part separately.

Firstly, take 21x⁶...using the product rule this intergrates like so (21/(6+1))x⁶⁺¹ = (21/7)x⁷ = 3x⁷

Second, e^kx always intergrates to (1/k)e^kx .........so -e^2x goes to (-1/2)e^2x.

1/x has the common intergral of lnx which must simply be learnt.

And finally, 6 intergrates to 6x.

We then collect all these parts and put them together so we get y=3x⁷-(1/2)e^2x-lnx+6x+C

Always remember that for intergration without limits you must always add C at the end.