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When tackling an unobvious integral question, first run through all the possible methods. I will now list the methods of integration: Substitution: could use this method, but it wouldn’t be particularly h...

When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √3" was the denominator of ...

y=(4x^2+1)^5                        y=u^5          u=4x^2+1

                                             y’=5u^4   (wrt u)  u’=8x

y’=40x(4x^2+1)^4

y’=40x(4x^2+1)^4=0             x=0  ...

Each part can be done separately, so x^2 becomes 2x, xy becomes dy/dx + y by product rule, y^2 becomes 2y(dy/dx) by chain rule, and 1 becomes 0. Hence the answer is 2x + y + (2y+1)dy/dx = 0, but the answe...

x^2=y+1 therefore 6y+2y+2=6 therefore 8y=4 y=0.5 sub in to either equation x=(3/2)^0.5