U substitution Definition and 54 Threads

In calculus, integration by substitution, also known as u-substitution or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards".

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  1. Saladsamurai

    U Substitution: Solve \int sec^3(2x)tan(2x) - Casey

    So I have another U substitution. \int sec^3(2x)tan(2x) this one is a little tricky for me. I have tried letting u= sec2x and tanx and 2x. 2x definitley gets me nowhere. I may be mistaken on the others. I will recheck them. I was also thinking of rewriting it as \int sec^4(2x)sin(2x)...
  2. Saladsamurai

    What is the Derivative of Arctan?

    I know this must be similar... \int \frac{e^x}{1+e^{2x}} should u=1+e^{2x}? Casey
  3. G

    Integration, u substitution, 1/u

    [SOLVED] Integration, u substitution, 1/u -- +C at the end of the integral solutions, I can't seem to add it in the LaTeX thing -- Homework Statement #1 \int\frac{1}{8-4x}dx #2 \int\frac{1}{2x}dx The Attempt at a Solution #1 Rewrite algebraically: \int\frac{1}{x-2}*\frac{-1}{4}dx Pull out...
  4. K

    U substitution for differentiation?

    How do I evaluate: d/dt sqrt [ t^4 + t^2 ]= 0 to get a max/min value. can I make a u substitution of some sort?
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