Barun Dasgupta
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 7 Evaluate :$\int \frac{\sin^{-1} \sqrt{x} -\cos^{-1} \sqrt{x}}{\sin^{-1} \sqrt{x} +\cos^{-1} \sqrt{x}} dx$ 6 Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers 3 A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$ 2 Fourier and half range series for $\sin x$ 2 proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$.

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### Questions (5)

 9 On Pythagorean Triplets 5 Fermat's Last Theorem - A query 4 Diophantine Equation $x^n + y^n =z^n (x2)$ 3 $x^n+y^n=z^n$ where $x,y,z$ are real numbers 1 Diophantine Equation $x^n+y^n=z^n$

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 11 inequality × 4 3 summation 7 integration 3 induction 4 differential-equations × 4 2 coordinate-systems × 2 3 calculus × 5 2 fourier-analysis 3 discrete-mathematics 2 fourier-series

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 Mathematics 559 rep 28 Physics 101 rep