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I'm sure this will be simple for someone, how do you go from the line I've highlighted (with the oversized arrow) to the next line. I can't see it. Question

Thanks Mike

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    That's only linearity of the integral: for any two integrable function $\;f,\,g\;$ , we have $$\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx$$ – 2017-02-06
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    Just notice $\frac{e^{2x}+1-e^{2x}}{e^{2x}+1}=\frac{(e^{2x}+1)-e^{2x}}{e^{2x}+1}=\frac{e^{2x}+1}{e^{2x}+1}-\frac{e^{2x}}{e^{2x}+1}$. – 2017-02-06

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We have that $$I = \int (\frac {e^{2x}+1 - e^{2x}}{e^{2x}+1}) \mathrm {d}x $$ $$= \int (\frac {e^{2x}+1}{e^{2x}+1} - \frac {e^{2x}}{e^{2x}+1}) \mathrm {d}x $$ $$= \int (1 - \frac {e^{2x}}{e^{2x}+1}) \mathrm {d}x $$

The fact that we can rearrange the terms and cancel out common terms is used here. Hope it helps.