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Let's first find the equilibrium position of the spring. When the mass is first attached the spring will oscillate like a simple harmonic oscillator, in the real world the oscillator will eventually settl...
1/(5 + 4i) * (5 - 4i)/(5 - 4i) = (5 - 4i)/41
You need to use a clever trick for this! Write ln(x) as 1ln(x), and use integration by parts:u=ln(x) v'=1u'=1/x v=xThen applying the formula we obtain∫ln(x)dx = xln(x) - ∫[(1/x)x] dx = ...
Differentiate implicitly on both sides with respect to x to get: 2=cos(y) • (dy/dx). Divide by cos(y) on both sides to get: dy/dx=2/cos(y). Use the trigonometric identity cos^2(y)+sin^2(y)=1 rearranged to...
We cannot dirrectly intergrate ln(x), so instead we intergrate 1ln(x) using intergration by parts.The formula for intergration by parts is: ∫ (udv/dx) dx = uv − ∫ vdu/dx dx .We le...
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