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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

From the format of the equation, we know this graph is a straight line because it follows the form, y=mx+c. The coefficent of x (the number before x) describes the gradient of the straight line or m. This...

Draw y=x^2+5. Draw the axes. Y to the sky (Y axis is vertical) and X across (X axis is horizontal). Then breakdown the equation. Firstly what power is the x to? x^2 means that the graph will have a U shap...

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...