X5 Parts
integration problem please help!?
integration of their use by the parties to resolve the definite integral int:. 0-1 From x5 ^ x dx 1 x S x5 dx 0 I hope you can understand! I tried using: u = 5 ^ x du = XLN (5) dx dv = x V = x ^ 2 / 2 but when I get to the integration of visual display (for the formula: UV - S VDU) are stuck with: S (x ^ 3In (5)) / 2 dx help! i ok! I have, but an important detail ... How did you get the int. 5 ^ x / (ln (5) = 5 ^ x / (ln (5) ^ 2 what this rule is if you can tell because I can not seem to figure that part .. all the things above are great though! But for me continue i have to know how integrated the last part ... please! thanks!
If you try to use u = x dv = (5 ^ x) dx, then you have du = dx v = (5 ^ x) / ln (5) (from the first derivative of x 5 ^ ^ is 5 x (ln (5)). Then do the following: int (x5 ^ x dx) = x 5 ^ x / ln (5) - Int ((5 ^ x) / ln (5) dx) = x 5 ^ x / ln (5) - 5 ^ x / (ln (5)) ^ 2 + C = 5 x ^ (ln (5) x - 1) / (ln (5)) ^ 2 + C is a indefinite integral yet so just plug the values required to solve. I hope that helped 
ADDITIONAL INFORMATION Remember that there is a formula for differentiation as d / dx (a ^ x) = A ^ x ln (a) and its inverse (primitive) for integration int (a ^ x dx) = (a ^ x) / ln (a) + C? This is practically a straight forward application of this formula. We have a full int ((5 ^ x) / ln (5) dx). We can rewrite this integral as int ((5 ^ x) / ln (5) dx) = (1/ln (5)) int (5 ^ x dx). We can do that because 1/ln (5) is simply a constant, so we can factor out and simplify the integral in this way. So now we are left with the same problem we had before, When we said that dv = 5 ^ x dx, remember? So now, as we see, As we have said before, that, after int (5 ^ x dx) evaluates to 5 ^ x / ln (5) + C. Now just multiply this by the constant factor eliminates: 1 / Ln (5) (5 ^ x / ln (5) + c) = 5 ^ x / (ln (5)) ^ 2 + C (C do not change because it is really irrelevant (in this exercise) - is only a number) Also be written as 5 ^ x / (ln (5)) ^ 2 + C = 5 ^ x / ln ^ 2 (5) + C. Need help?
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