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This is a common question among A-Level Maths students, as integration by parts requires 2 things: 1. Something to integrate ; 2. Something to differentiate. In ln(x), we can immediately see that ln(x) is...

12th term = a + (12 - 1)*d = 2 + 11(3) = 35

Sum (9) = 9/2 [2(2) + (9 - 1)*3] = 9/2 [28] = 252/2 = 126

Adding the fractions on the RHS of the equation in the usual way gives 

A/(2-x) + B/(1+3x) = (A(1+3X) +B(2-X))/((2-X)(1+3X)) = (5x +4)/((2-x)(1+3x)) 

This gives an expression for the origina...

In this exercise I have to find the coordinates of the vertex of the parabola. Given the general equation y= ax^2 + bx + c , the value of a is 2, the value of b is -4 and the value of c is 1.

In or...

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x²-2ax+8. At point B, <...