Solve \({e^{2\log_ex}} = 4\)
Solve \({e^{2x}} - 2{e^x} - 8 = 0\)
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Differentiate \(y = \dfrac{{\log_ex}}{x}\)
Differentiate \(y = \log_e\sqrt {\dfrac{{x + 1}}{{x - 1}}} \)
Find the equation of the tangent to the curve \(y = \log_e({x^2} - 1)\) at \(x=2\)
Find the stationary point on the curve \(y = {x^2}\log_ex\) and determine its nature
\(\int\limits_0^1 {\dfrac{{{x^2}}}{{{x^3} + 1}}dx = } \)
Differentiate \(y = (x + 1)\log_e(x + 1)\) and hence evaluate \(\int\limits_0^1 {\log_e(x + 1)} \,dx\)
Determine the area between the curve \(y = \dfrac{{2x}}{{{x^2} + 1}}\) the \(x\)-axis and the line \(x=2\)
Find the area bounded by the curve \(y = \dfrac{1}{x} + 1\) the \(y\)-axis and the lines \(y=2\) and \(y=3\)
Find the equation of the normal to the curve \(y = \log_5(x + 1)\) at \(x= 0\)
\(\int\limits_1^2 {{2^{2x}}dx} = \)
\(x = 2\)
