Mathematics

$$\displaystyle \int \dfrac{e^{-x}}{1+ e^{-x}}dx$$ $$=$$  $$-p \log (1+e^{-x})+C$$ then p =


ANSWER

1


SOLUTION

$$Let\>1+e^{-x}=t\\\therefore\>-e^{-x}dx=dt\\\therefore\>\int\>(\frac{1}{t})dt\\=-logt+C\\=-log(1+e^{-x})+C$$

View Full Answer

Its FREE, you're just one step away


One Word Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Evaluate : $$\displaystyle\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx.$$
  • A. $$\displaystyle \sin \sqrt{x}.$$
  • B. $$\displaystyle 2\sin x.$$
  • C. $$\displaystyle 2\sin \sqrt{x}/3.$$
  • D. $$\displaystyle 2\sin \sqrt{x}.$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
$$\displaystyle \int sin^{-1}\sqrt{\frac{x}{a+x}}dx=\ldots\ldots$$
  • A. $$(a+x)tan^{-1} \sqrt{x/a}+\sqrt{ax}+c$$
  • B. $$(a+x)cot^{-1} \sqrt{x/a}+\sqrt{ax}+c$$
  • C. $$(a-x) cot^{-1}\sqrt{x/a}-\sqrt{ax}+c$$
  • D. $$(a+x)tan^{-1} \sqrt{x/a}-\sqrt{ax}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate the following integrals:$$\displaystyle \int {\dfrac{3}{\sqrt{7x-2}-\sqrt{7x-5}}.dx}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
Evaluate : $$\displaystyle \underset{0}{\overset{\infty}{\int}} \dfrac{dx}{(1 + x^2)^4}$$
  • A. $$\dfrac{\pi}{32}$$
  • B. $$\dfrac{3 \pi}{32}$$
  • C. $$\dfrac{7 \pi}{32}$$
  • D. $$\dfrac{5 \pi}{32}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer