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First identify that integration by parts is required. Then seperate the integration so u = ln(x)     dv/dx = x then, du/dx = 1/x  v = (1/2)x^2 . And using the integration by parts formula with these subst...

This is a very common type of question that might be asked in an exam and there are 3 methods we could use to solve this; by substitution, by elimination (or subtraction) or by using straight line graphs....

BIDMAS 

Following BIDMAS, multiply the bracket out before the addition of the 2y.

3y(5y+3) = 15y²+9y 

adding the 2y gives the calculation of 15y² + 9y +2y = 15y<...

y is a function of x₁ and x₂. We are asked to derive y with respect to x₁, meaning that x₂ remains constant. 

Note that y' is the deriva...

First we need to change the limits, and by plugging in 1 and 0 to our substitution we find that the limits for u are arctan(1) and arctan(0) (or pi/4 and 0). Then we need to substitute for dx, and by diff...