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In reality there's no way to know for certain and in fact some integrals can actually be proven to be impossible but they won't give you those in the exam. There's only really two main methods that you'll...

Ans: dy/dx = 15x^2 + 16x^-5 + b To solve for the first part of the right hand side, remember to bring the power of 3 forward and multiply, then reduce our power by 1 to leave 15x^2. For the second part, b...

5+3=8 80/8= 10 therefore one part = 10 john receives 5 parts, simon receives 3 john=5x10=50 simon=3x10=30

If we are given an integral where the integrand (stuff in between the integral symbol and dx) is a product of two separate functions. we then allow whichever of the functions that will be easier to differ...

By using our laws of Indices we know: x^5 * x^12 = x^17 and x^4 * x^4 = x^16

Therefor (x^5 * x^8)/(x^4 * x^4) = x^17/x^16 = x^1 = x.