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Integrating 1/x (Reciprocal Function)

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Explanations 1

Let's say we want to find a function f(x)f(x)f(x) that satisfies df(x)dx=f(x)\frac{\text df(x)}{dx}=f(x)dxdf(x)=f(x) Or f(x)=lim⁡h→0f(x+h)−f(x)hf(x)=\lim_{h\to0}\frac{f(x+h)-f(…
By Tim Ratigan, Moor Xu

Problems 5

Let f(x)=1+12x+14x2+18x3+…f(x) = 1 + \frac12 x + \frac14 x^2 + \frac18 x^3 + \dotsf(x)=1+21x+41x2+81x3+… for −1≤x≤1-1\le x\le 1−1≤x≤1. Find e∫01f(x)dxe^{\int_0^1 f(x) dx}e∫01…
∫01x3−3x2+5x−3 dx\int^1_0\frac{x^3-3x^2+5}{x-3}\,dx∫01x−3x3−3x2+5dx
Compute ∫1e12x dx\int_1^e \frac1{2x} \, dx∫1e2x1dx as a decimal to the nearest tenth.
Integrate ∫1+x+xx dx\int \frac{1 + \sqrt x + x}x \, dx∫x1+x+xdx.
∫311x\displaystyle\int_3^{1}\frac{1}{x}∫31x1