1. The right direction - you've basically done...

... where (key in spoiler) ...

Spoiler:

... but you've not finished solving the bottom row for f'(x)...

7 ln x you've multiplied by f(x) but not the other term (the one cancelling down to 7).

Yes - so you could draw a similar picture?

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!