How Do I Compute the Integral Using u-Substitution?

[kyu]

what method should i use? i tried

u = x - 4
du = dx

i can't continue. enlighten me please

 

[STEMucator]

It looks like a pretty tedious partial fraction expansion.

 

[Mark44]

what method should i use? i tried

u = x - 4
du = dx

i can't continue. enlighten me please

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.

It looks like a pretty tedious partial fraction expansion.

An ordinary substitution will do the trick.

 

[lurflurf]

It looks like a pretty tedious partial fraction expansion.

It is neither tedious nor particularly helpful.

$$\frac{2x+1}{(x-4)^6}=\frac{2(x-4)+9}{(x-4)^6}$$

 

[NasuSama]

It is neither tedious nor particularly helpful.

$$\frac{2x+1}{(x-4)^6}=\frac{2(x-4)+9}{(x-4)^6}$$

This is quite efficient to compute the integral. ;)

 

[mafagafo]

This is quite efficient to compute the integral. ;)

What do you mean?

 

[LCKurtz]

This is quite efficient to compute the integral. ;)

What do you mean?

He means it is easy.