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 1 + (1 + (1 + (1 + (1 + ...)^-1)^-1)^-1)^-1

This pattern goes infinitely.

The first step to this question, is to observe. Observe the patter...

First separate the variables so that the left side of the equation is an expression only in terms of y and the right side only in terms of x.exp(y)dy=sin2x dxSecondly both sides have to be integrated to o...

2^{3x - 1} = 3log₂(2^3x-1) = log₂(3)3x - 1 = log₂(3)3x = 1 + log₂(3)x = ¹/₃ + ¹/₃log₂(...

Apply the double angle formula to cos2x to yield the requested result.
cos2x = 2cos^2(x) - 1
Spot that the question asks us to prove the value of cos^2(x) when integrated, and that we can move t...

First, manoeuvre variables so that we can integrate the equation.
1/(x-6)^(1/2) dx = -2 dt
Integrate the equation and add the constant.
2(x-6)^(1/2) = -2t +c
Solve for t.
t = -(x-...