Intergration question. 3 ln (cos t)

[blazekid43]

Integrate:
3 ln (cos t)

To me it feels like the answer should be 3/cos t.
Because the question isn't 3 ln (t)(cos (t)). So I'm not really sure how I should integrate this.

 

[Deleted member 4993]

Integrate:
3 ln (cos t)

To me it feels like the answer should be 3/cos t.
Because the question isn't 3 ln (t)(cos (t)). So I'm not really sure how I should integrate this.

This is actually a very hard integration problem - the answer involves special functions and complex functions.

Double check your original problem.

 

[blazekid43]

This is actually a very hard integration problem - the answer involves special functions and complex functions.

Double check your original problem.

I actually got it from a problem I've been trying to solve . Its part B to the question "find the length of the curve"

EDIT: opps, I think I have to differentiate 3 ln (cos t) first, not integrate. My bad. But I still don't know how to do that.

 

[Deleted member 4993]

I actually got it from a problem I've been trying to solve View attachment 3121. Its part B to the question "find the length of the curve"

EDIT: opps, I think I have to differentiate 3 ln (cos t) first, not integrate. My bad. But I still don't know how to do that.

I thought so....

ln[cos(t)] is a compound function like f[g(x)]. You need to use chain-rule.

\(\displaystyle \displaystyle \frac{df}{dx} \ = \ \frac{df}{dg} . \frac{dg}{dx}\)

 

[fcabanski]

-sin(t)*3/cos(t) = -3sin(t)/cos(t) = -3*tan(t)