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Integral of ln x

xln(x) - x

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The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form rexp(iTheta), where r>0 and -pi < theta <= pi. By using the form rexp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.

Find the integrating factor of the following first order ODE: dx/dt = -2tx +t.

Find the general solution to the differential equation d^2x/dt^2 + 5 dx/dt + 6x = 4 e^-t

a) Show that d/dx(arcsin x) = 1/(√ (1-x²)). b) Hence, use a suitable trigonometric substitution to find ∫ (1/(√ (4-2x-x²))) dx.

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