# HARD Mathematic examination question

HARD!! Mathematic examination question

## Homework Statement

$$\int_0^2\int_π/3^π (x^2*\sec^3 x^3 -12\ /\sqrt{e^π+x^2 +2x})\,dx\,d(theta)$$ ## Homework Equations

I could not find any relevant questions on the web, however this is simply a question from an exam written the 14th of October 2013 regarding multiple integrals

## The Attempt at a Solution

I attempted to use trig substitution, substituting x=tan(theta), dx=sec^2(theta) d(theta)
to no progress I gave up ... then I wondered whether i should have subsituted u=π-x ∴ x=π-u
but this led to bigger problems... I have sincerely attempted to solve this problem for a day now, please help, I would trully appreciate it...

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So it's ##\displaystyle\int_0^2\left(\int_{\frac\pi3}^\pi\left(x^2\cdot\sec^3 \left(x^3\right)-\dfrac{12}{\sqrt{e^\pi+x^2+2\cdot x}}\right)\cdot\mathrm{d}x\right)\cdot\mathrm{d}\theta##? That ... sounds like a strange integral, especially considering the lack of any ##\theta## in the integrand. Try using the fact that ##\displaystyle\int\left(f+g\right)=\int f+\int g##, then use a couple substitutions. You might have to complete the square in the square root.

'm terribly sorry, its my first time so I made a slight mistake in the equation... Its supposed to be a double integral, not separated by brackets. Also it should read after the second integral [x^2.Sec^3(x^3 -12)/√e^π+x^2 -2x] and finally dx.d(theta)

haruspex