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Chain Rule & Integration by Substitution

Review question

Can we carry out these three tricky integrals?
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Ref: R8778

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Suggestion

(a)(ii) Find \(\displaystyle \int \frac{1}{\sqrt{2x - x^2}} \:dx\).

Could we try completing the square on the denominator?

Evaluate \(\displaystyle \int_0^{\pi/4} \sec^4 x \:dx\).

What do we get if we differentiate \(\tan x\)?