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Integrate x/(x^2+2)

0.5Ln(x^2+2)+ C

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Answered by Rajan S. • Maths tutor

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Let w, z be complex numbers. Show that |wz|=|w||z|, and using the fact that x=|x|e^{arg(x)i}, show further that arg(wz)=arg(w)+arg(z) where |.| is the absolute value and arg(.) is the angle (in polar coordinates). Hence, find all solutions to x^n=1 .

x = 1 is a solution for the curve y = x^3-6x^2+11x-6, find the other solutions and sketch the curve, showing the location of any stationary points.

How do I use simple integration?

Take the polynomial p(x)=x^4+x^3+2x^2+4x-8, use the factor theorem to write p(x) as two linear factors and an irreducible quadratic. An irreducible quadratic is a quadratic that can not be factorised.

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