# Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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### Strange behaviour of integrals with Cos, Sin, and Exp

Bug introduced in 8.0.4 or earlier and persisting through 14.0 During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would ...
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### Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
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### Reduce: Var is not a valid variable

Bug introduced in 7.0 and persisting through 13.1 or later. Fixed in 13.2.0 or earlier. I am trying to integrate the following but it returns a Reduce::ivar ...
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Consider the following two polynomials: f1[t_] := t^3 - 1 f2[t_] := t^3 + 3t - 1 Both of these polynomials have a single real root: $f_1(t)$ at $t = 1$, and $... • 15.2k 5 votes 0 answers 233 views ### Total variation integration of a discontinuous function This question derives from this one, about mathematics and Maple. Consider the following discontinuous function: ... • 41.3k 5 votes 0 answers 359 views ### How to verify the convexity of a function? I have an optimization problem with the following objective function in$(x,y)$$$A\log \left(\sum_{i=1}^n x_i\right)+\log\left(1-\frac{f}{n}\left(\sum_{i=1}^n\frac{x_i}{y_i}\right)\right)$$ where$...
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Bug introduced in 9.0 or earlier, and fixed in 10.2 I noticed a bug in Mathematica. It computes incorrectly a definite integral ...
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### Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

Saw this post and noted that it was posted back in 2013. Just tried V11.3 and got no analytic solution. Just wondering if there is a way for Mathematica to give the desired result? Machine VS Human ...
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### Trigonometric integral with assumptions fails

Consider the following integral Assuming[Element[{n, m}, Integers] && n >= 0, Integrate[Cos[ϕ]^n Exp[I ϕ m], {ϕ, 0, 2 π}]] ...
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