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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...

Firstly, you need factorise.a = 3 b = 13 c = 14Find 2 numbers which add to make b(13) and multiply to make ac(42). These numbers are 6 and 7You can now split up the x coefficient to: 3x^2 + 6x + 7x + 14. You...

To factorise an expression such as x 2 - 8x + 15, you need to look for two numbers that add up to make -8 and multiply to give 15. The only option in this case is -5 and -3 (-5)+(-3)=-8and (-5)x(-3)=15as two...

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-...

Use product rule i.e. (uv)'=u'v+uv'Set u=e^x and differentiate to find u'=e^x Set v=cosx and differentiate to find v'=-sinxTherefore (uv)' where uv=e^xcosx =e^xcosx + e^x(-sinx)=e^xcosx - e^xsinx=e^x(cosx -s...