anonymous 5 years ago solve integral (1-tan^2(x))

1. anonymous

$\int\limits_{?}^{?}1-\tan ^{2}x=\int\limits_{?}^{?}1-(\sec ^{2}x-1)$

2. anonymous

1-tan^2(x) is a nice Identity... do you know what it is ?

3. anonymous

$=\int\limits_{?}^{?}2-\sec ^{2}x$

4. anonymous

2x-tanx+C

5. anonymous

just to let you know uzma, if you eliminate the _{}-{} part after "int" the limits of the integral will go away like this $\int\limits$

6. anonymous

oh thanks, i dint try it :)

7. anonymous

np :)

8. anonymous

$\int\limits$

9. anonymous

Lao, to remember the integrals of trig, you need to know the derivatives of them very well

10. anonymous

right ?:)

11. anonymous

for this one, d/dx(tan(x)) = sec^2(x) was the one tat uzma referred to

12. anonymous

@ uzma fantastic !

13. anonymous

thanks

14. anonymous

another one you will see a lot is things like $\int\limits -\csc(x)\cot(x) dx$

15. anonymous

if you try to do u-substitution or integration by parts, it will be a tough one, but if you remember d/dx csc(x) = -csc(x)cot(x) then we know that the integral that I showed you will have an ans csc(x) + C