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Step 1. Draw Pascal's triangle to find the coefficients. 1; 1 2 1 ; 1 3 3 1 ; 1 4 6 4 1. As you can see, each row starts and finishes with 1. The numbers in between are worked out by adding the two numbers o...

The first step is to prove that the result is true for n=1.The second step is to assume that the result is true for n=k where k is any positive integer.The third step is to prove that the results is true for...

First split up the fraction into partial fractions as this is more easily integrated. It can be seen that the denominator has factors y and (3y+2), therefore we can say the original fraction is equal to part...

Firstly we integrate x^2 with respect to x which is (x^3)/3 as we integrate polynomials by adding a power then dividing by that power, (x^n+1)/n+1.Then we multiply by the 5 we have from earlier which gives u...

Split into partial fractions: (3x +2) / (x 2 - 5x +6) = A / (x-3) + B / (x-2) => 3x + 2 = A(x-2) + B(x-3) let x = 2: 8 = -B => B = -8 let x = 3: 11 = A => A = 11 Now we can integrate f(x) = 11 / (x-...