Get Integration By Substitution

The purpose in using the substitution technique is to rewrite the integration problem in terms of the new variable so that one or more of the basic integration formulas can then be applied. Although this approach may seem like more work initially, it will eventually make the indefinite integral much easier to evaluate.

u substitution is another method of evaluating an integral in an attempt to transform an integral that doesn't match a known integral rule into one that does. ... integral(f(g(x))g'(x)dx) = integral(f(u) du), say you have some function x * sin(x^2+5) that you want to evaluate the integral of using this method.

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A good rule of thumb to follow would be to try u-substitution first, and then if you cannot reformulate your function into the correct form, try integration by parts. ... Some definite integrals have no way to solve other than integration by parts, by finding the same integral on both sides of the equation.

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-Substitution essentially reverses the chain rule for derivatives. In other words, it helps us integrate composite functions. When finding antiderivatives, we are basically performing "reverse differentiation." Some cases are pretty straightforward.

A u-sub can be done whenever you have something containing a function (we'll call this g), and that something is multiplied by the derivative of g. That is, if you have f(g(x))g (x)dx, use a u-sub.

u substitution is another method of evaluating an integral in an attempt to transform an integral that doesn't match a known integral rule into one that does. ... the substituted integral would be 1/2 * integral(sin(u)*du) = - 1/2 cos(u) + C = -1/2 cos(x^2+5) + C.

Evaluating a definite integral using u-substitution Use u-substitution to evaluate the integral. Since we're dealing with a definite integral, we need to use the equation u = sin x u=\\sin{x} u=sinx to find limits of integration in terms of u, instead of x.