Integration Question (1 Viewer)

[conics2008]

Hi, I just started Integration today, and was wonderin with this rule..

it goes like this

S f ' (x) / f (x) dx = ln | f(x) |

right ?


therefore when u apply this here

S sec^3 (x) tan (x) dx

= 1/cos^3 (x) x sin(x) / cos(x) >> sin(x) / cos^4 (x) right ???

therefore f(x)= cos (x) and f ' (x) = -sin (x)

then - S - sin(x)/cos^4 (x) = -ln | cos^4 (x) | ?????????????????

is this correct or not.. in the book is wrong but im abit confused with that formula or pattern... I seem to get it right with all but this question is confusing me.. Thanks =)

 

[Affinity]

everything is correct up to here:
- S - sin(x)/cos^4 (x)

but you see..
while S f ' (x) / f (x) dx = ln | f(x) |
S f ' (x) / [f (x)]^4 dx Is Not ln | [f(x)]^4 |

 

[conics2008]

ohh ok so it doesn't apply there.. no high powers i see i see thanks. cuz this question is pissin me off..

how on earth do you learn table of indefinite integrals.. there are soo many, i basically have to look at the table and see where i have to use it... ??

is this the only way ???

I'm good with sub but never had to refer to a the table...

 

[tacogym27101990]

回复: Integration Question

you dont have to remember them, you get them in the test.
just understand how to apply them

 

[Affinity]

it should be blatantly obvious, saying
- S - sin(x)/cos^4 (x) = -ln | cos^4 (x) |
is like saying
S 1/x^4 = - ln |x^4|

hmm you derive the table....

 

[tacogym27101990]

回复: Integration Question

once u get to

S sinx/cos^4x dx

just let u = cosx

 

[Slidey]

Re: 回复: Integration Question

Deriving the table of standard integrals in your spare time at least once is good practice. Most (or all) of them should be easily doable with 4u techniques, if somewhat tedious.