**Integration marathon for MX2 2018**

Post integration questions within scope of MX2

First question: (from pikachu975)

Integrate 1/[(sinx)sqrt(sin2x)]

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Post integration questions within scope of MX2

First question: (from pikachu975)

Integrate 1/[(sinx)sqrt(sin2x)]

Hint: expand and substitutepikachu975 said:

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Further hint: take something out of the root and simplify, then substituteHint: expand and substitute

Wait the sinx is on the denominator. It's basically the BOS trial question

Yup. FYI the mistranscribed integral is equivalent to 1/root(2) integral of root(tanx) which has been calculated to exhaustion.Wait the sinx is on the denominator. It's basically the BOS trial question

Yup. FYI the mistranscribed integral is equivalent to 1/√2 integral of √tanx which has been calculated to exhaustion.

The rest is trivial.

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For , define .

(a)Show that f(x) is decreasing. Write down the maximum value of f(x).

(b)Find .

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For , define .

(a)Show that f(x) is decreasing. Write down the maximum value of f(x).

(b)Find .

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I don't think

Also spoiler for the one above:

Do the same substitution as the one above it

is the right substitution for that.

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This one is fairly straight-forward.

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That being said is there a way of doing it using only 4U methodssik MIT steal