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To solve this integral you should use the integration by parts formula, which is uv - integral of vu'. First let x^2 be u, therefore u'(the differential of x^2) = 2x, v' = e^x and therefore v (integral of...

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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...