- #1
That works. Keep in mind that if u = x -4, then x = u + 4. Replace x and dx in the integral with what you have for u and du, and you'll get an integral that's easy to work with.kyu said:what method should i use? i tried
u = x - 4
du = dx
i can't continue. enlighten me please
An ordinary substitution will do the trick.Zondrina said:It looks like a pretty tedious partial fraction expansion.
Zondrina said:It looks like a pretty tedious partial fraction expansion.
lurflurf said:It is neither tedious nor particularly helpful.
$$\frac{2x+1}{(x-4)^6}=\frac{2(x-4)+9}{(x-4)^6}$$
NasuSama said:This is quite efficient to compute the integral. ;)
NasuSama said:This is quite efficient to compute the integral. ;)
mafagafo said:What do you mean?
Numerical integration involves approximating the value of an integral using numerical methods, while analytical integration involves finding the exact solution using mathematical techniques such as substitution and integration by parts.
The most commonly used method of integration is the fundamental theorem of calculus, which states that the integral of a function can be evaluated by finding its antiderivative.
The method of integration used depends on the complexity of the integrand and the techniques that are available for solving it. Some common methods include substitution, integration by parts, partial fractions, and trigonometric substitution.
Yes, it is possible to use more than one method of integration for a single integral. This is often necessary for integrands that are too complex to be solved using a single method.
Yes, numerical methods of integration have limitations such as being prone to error and requiring a lot of computation for complex integrals. They also cannot provide exact solutions like analytical methods can.