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 Feb2 comment Examples of double surface integrals I found these online tutorials to be very good: tutorial.math.lamar.edu/Classes/CalcIII/… Feb2 revised Find a value for a number to the power of a complex number added 1 character in body Jan31 revised Trigonometric integral (arctg) added 13 characters in body Jan24 revised The meaning of dot centered vertically, as in $3\cdot 5$ added 12 characters in body Jan24 answered The meaning of dot centered vertically, as in $3\cdot 5$ Jan22 awarded Yearling Jan21 comment Logarithms of Negative Numbers $\log z=\log|z|+i\text {Arg} z$ if you take the principal branch. Exponentiating both sides gives $z=|z|e^{i\text{Arg}( z)}$ as you might hope to expect. Jan20 comment Computing the integral of $\int \frac{25x^2}{(x+3)(x-2)^2}\,dx$ what is "impartial differentiation" ? Jan20 comment Proof of $\cos(y)$ and $\sin(y)$ using $e^{iy}$ A simple case of substitution followed by simplification will achieve what you want. Jan20 revised Solving $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y }=1$ deleted 19 characters in body Jan20 comment Solve the integral $\int \frac{x^3+1}{x^2+7x+12}\, dx$ What have you tried so far? Any ideas what might work? Jan20 comment Does $\int_0^\infty \sin(x^{2/3}) dx$ converges? Maybe $$I=\Im\int_0^\infty e^{ix^{2/3}}dx,$$ and then use the error function. Looks divergent. Jan20 revised Closed form for $\prod_{k=1}^n (a+k^2)$ edited body Jan20 revised Closed form for $\prod_{k=1}^n (a+k^2)$ deleted 2 characters in body Jan20 answered Closed form for $\prod_{k=1}^n (a+k^2)$ Jan20 awarded Organizer Jan20 revised Expansion Of A algebric term added 80 characters in body; edited tags Jan20 comment Equation $e^{\frac{1}{x}} - x =0$ Could we use Lagrange inversion theorem here? en.wikipedia.org/wiki/… c.f. also @ PM's comment and @ Lukas' answer. Jan20 revised Finding the definite integral of a function that contains an absolute value added 227 characters in body Jan19 comment Is there a name for functions “opposite in nature” to orthogonal functions? Thanks David. Are you using the property that the square of a function is always positive here? What if $g_n^2$ is not always positive, e.g. $g_n(x)=\sqrt{h(x)}$ for some $h$ whose image is $[-a, a]$ ?