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krypton Group Title y=d/dx integralcosx to 0 t/(1+t)dt 2 years ago 2 years ago Edit Question Delete Cancel Submit

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1. krypton
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$d/dx \int\limits_{0}^{cosx} \frac{ t }{ 1+t } dt$

• 2 years ago
2. Outkast3r09
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$\frac{cosx}{1+cosx}$

• 2 years ago
3. krypton
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how did u do it?

• 2 years ago
4. Zekarias
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@Outkast3r09 I think u made a miss take in your first step (While u made the integral)

• 2 years ago
5. Outkast3r09
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the derivative of an integral is simply the integral itself with the variables in other words ... integrals and derivatives cancel eachother out

• 2 years ago
6. Outkast3r09
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$\frac{cosx}{1+cosx}$is your answer

• 2 years ago
7. Zekarias
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It should be$\cos(x)-\ln(1+\cos(x))$

• 2 years ago
8. Outkast3r09
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|dw:1349804491261:dw|

• 2 years ago
9. Zekarias
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Now take the derivative

• 2 years ago
10. Outkast3r09
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it shouldn't be anything @ zekarias

• 2 years ago
11. Outkast3r09
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@zekarias ... you don't need to do anything

• 2 years ago
12. Zekarias
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What u get finally?

• 2 years ago
13. krypton
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so the answer is just cosx/1+cosx ?

• 2 years ago
14. Outkast3r09
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yes

• 2 years ago
15. krypton
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thanks,wolfram gives me the same answer,just wanted to make sure how it was done

• 2 years ago
16. Outkast3r09
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it's just simply knowing how an integral work... there is a lot of work to do it zekarias way but if you just know that the the derivative on an integral will bring you back to the f(x) within the integral... that's all you need to know(This works anytime the lower limit is some real number) because if you think about it.... |dw:1349804918350:dw| if you take the derivative of f(n)... you'll always get zero

• 2 years ago
17. krypton
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oh thanks alot sweedy :)

• 2 years ago
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