Mathematics

Integrate $$\dfrac{dx}{[1-e^{2x}]^(1/2)}$$


SOLUTION
Let $$e^{2x}=t$$
$$2e^{2x}dx=dt$$
$$\displaystyle dx=\frac{dt}{2e^{2x}}$$
Now putting the value of $$dx$$ in gven question we get
$$\displaystyle \int\frac{dt}{(1-t)t}=\int\frac{dt}{t}+\int\frac{dt}{1-t}$$
$$\displaystyle \int\frac{dt}{(1-t)t}=$$ $$\displaystyle \ln{t+ln{(1-t)}}$$
Now putting the value of t we get
$$\displaystyle \int\frac{2dx}{(1-e^{2x})}=$$ $$\displaystyle 2x+ln{(1-e^{2x})}$$
View Full Answer

Its FREE, you're just one step away


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

Realted Questions

Q1 Subjective Medium
Evaluate $$\displaystyle\int^1_0\dfrac{dx}{\sqrt{1-x^2}}$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
What is the value of $$\int_{0}^{a}\dfrac{x-a}{x+a}\ dx$$?
  • A. $$a+2a\log 2$$
  • B. $$2a\log 2-a$$
  • C. $$2a\log 2$$
  • D. $$a-2a\log 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Integrate with respect to $$x$$:
$$2x^{2}e^{x^{2}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate:
$$\displaystyle\int { \left( \dfrac { x\cos { x } +\sin { x }  }{ x\sin { x }  }  \right) dx }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Hard
Solve :
$$\int \dfrac{1}{x}\sqrt{\dfrac{x+1}{x+1}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer