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Integrate by parts, identifying that dv/dx = 1, u = ln(x) and therefore v = x and du/dx = 1/x. Sub into the parts equation to find the answer to be xln(x) - x + c.

The sine rule is a very powerful tool used in mathematics to calculate unknown sides and angles of triangles when we only know some of the information.

For example if we have a triangle and we know...

You say you are familiar with the product rule i.e. f(x)=u(x)v(x) f'(x)= u(x)v'(x)+v(x)u'(x) (Equation 1)

OK so why don't we try applying that here let's try splitting the function in this proble...

If the two parametric equations have the form x = at + b and y = ct + d then the first step is to rearrange one to make the parameter 't' the subject. We then substitute this equation for 't' int...

dy/dx= (x+2y)/(8y-2x)