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I need derivative and integral problems in many numbers (I prefer >100 questions, multiple sources are okay).

Scope: Start from high school material then raise to pre-college. Derivative, trigonometry derivative, indefinite integral, definite integral. Partial integral is okay, but not too much. Logarithmic, natural, etc. are okay also.

I also prefer difficult question like these:

Trigonometric function integration: $\int_0^{\pi/2}\frac{dx}{(a^2\cos^2x+b^2 \sin^2x)^2}$

A definite integral $\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx$

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$

Integral ${\large\int}_0^1\left(-\frac{\operatorname{li} x}x\right)^adx$

Even this one is okay too:

Prove ${\large\int}_{-1}^1\frac{dx}{\sqrt[3]{9+4\sqrt5\,x}\ \left(1-x^2\right)^{2/3}}=\frac{3^{3/2}}{2^{4/3}5^{5/6}\pi }\Gamma^3\left(\frac13\right)$

Community
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làntèrn
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1 Answers1

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I can recommend http://integralsandseries.prophpbb.com board. There are lots of interesting and nontrivial integrals, solved in details, often with several different approaches.

Take a look at forums Contests, Computation of Integrals.

I can also recommend reading Victor Moll's papers on integrals (e.g. these ones).

Vladimir Reshetnikov
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