## wendo Group Title 1. integral sin x/(cos x )^2= ? 2. integral (2-3t)^6 dt=? 2 years ago 2 years ago

1. dpaInc Group Title

for the first one, u=cosx

2. dpaInc Group Title

second one u=2-3t

3. lgbasallote Group Title

this doesnt seem like a u-sub problem @dpaInc looks like that basic application of general power formula

4. Romero Group Title

@lgbasallote Not for the first one

5. dpaInc Group Title

not necessarily but i like to do it so I don't miss the derivative of 2-3t...

6. lgbasallote Group Title

me too...that formula is too confusing :/ kinda like doing limits to find derivative

7. dpaInc Group Title

and @Romero , yes there's more than one way to skin this cat.. for the first one, the integrand can be rewritten as secxtanx

8. wendo Group Title

from my caculation first one is 1/cosx+c second one is -(2-3t)^7/21 +c is that right

9. lgbasallote Group Title

i think there should be a negative on #1

10. lgbasallote Group Title

*think*

11. campbell_st Group Title

looks like a nice simple substitution to me... but I'm still waiting for the rooster eggs to roll off the roof

12. lgbasallote Group Title

#2 seems right though @campbell_st whatis it with you and eggs :p

13. Romero Group Title

Second one is right. You just wrote it weird so it looks like the ^7 is getting divided by 21

14. wendo Group Title

why #1 is negative?

15. Romero Group Title

derivative of cos will give you a negative so when you do the chain rule you will need to cancel that negative with another one.

16. quarkine Group Title

these are too basic...perhaps u need to revisit the integration methods... 1/cosx and ((2-3t)^7)/(-3*7)

17. freckles Group Title

$\int\limits_{}^{}\frac{\sin(x)}{(\cos(x))^2} dx ...u=\cos(x) =>du=-\sin(x) dx ......\int\limits_{}^{}\frac{-du}{u^2}=-\int\limits_{}^{}u^{-2} du$ $\int\limits_{}^{}(2-3t)^6 dt....u=2-3t=> du=-3 dt .....\int\limits_{}^{}u^6 \frac{du}{-3}$

18. .Sam. Group Title

#2 $\int\limits (2-3 t)^6 \, dt$ u==2-3t, du=-3dt $-\frac{1}{3}\int\limits u^6 \, du$ $-\frac{u^7}{21}+c$ $-\frac{(2-3 t)^7}{21} +c$