Integrals Example Number 8 All right continuing on another integral problem, we have 2/x3/4 – 3/x2/3 dx. The first thing we’re going to do is convert this to none fractions since fractions are difficult to deal with than numerical. We’re going to do that. If I’m moving the denominators to the numerator and flipping the signs on this exponent here from positive to negative. That’s just of all that you can apply. I demonstrated that in previous video so this is going to be 2x-3/4. We can do that -3x-2/3 if we can do that. So that’s how we convert integral and then we can integrate. So we’re going to have our x down here looking at this term x we add one to the exponent negative ¾ + 1 is positive ¼ and then we’re going to divide the coefficient by the new exponent 2 over1/4. Then we’re going to do the next term 5dx- 2/3+ 1 = 1/3 and then 3 the coefficient over the new exponent 1/3 + 2 as the constant. So the thing we have to do now is simplify this new equation. We want to simplify these fractions. Again when we do that instead of dividing by fractions we can multiply by its inverse instead of 2 ÷ ¼. We can say 2x 4/1. So instead of 2 over ¼, that’s the same thing as saying 2 x 4/1. The answer to that of course is 8. So the answer here is 8x1/4 – 3÷ 1/3 is the same as 3 x 3/1 and dividing by the fraction we multiply and for both of the fraction 3 x 3/1 is 9 so minus 9x 1/3 + c. That’s all the answer there.