Mathematics

# Solve: $\displaystyle \int { \dfrac {dx }{ e^x+e^{-x} } }$

##### SOLUTION
$\displaystyle \int \frac{dx}{e^{x}+e^{-x}}$

$\displaystyle \Rightarrow \int \frac{e^{x}}{e^{2x}+1}dx\Rightarrow \int \frac{d(e^{x})}{(e^{x})^{2}+1}$

$\displaystyle \Rightarrow \int \frac{dz}{z^{2}+1}$   [let z = $e^{x}$ ]

$\displaystyle \Rightarrow tan^{-1}(z)+c$    [c is arbitrary constant]

$\displaystyle \Rightarrow tan^{-1}(e^{x})+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Suppose that F(x) is an antiderivative of f(x)$\displaystyle =\frac{\sin x}{x},x> 0$ then $\displaystyle \int_{1}^{3}\frac{\sin 2x}{x}$ can be expressed as
• A. $\displaystyle \frac{1}{2}\left ( F\left ( 6 \right )-F\left ( 2 \right ) \right )$
• B. $\displaystyle \frac{1}{2}\left ( F\left ( 3 \right )-F\left ( 1 \right ) \right )$
• C. $\displaystyle 2\left ( F\left ( 6 \right )-F\left ( 2 \right ) \right )$
• D. $F(6) - F(2)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\int_{}^{} {\frac{1}{{\sqrt {1 + x.} }}\,dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle \int_{0}^{3}x^2 \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate $\int_{0}^{\pi}e^{|\cos x|}\left (2\sin \left (\dfrac {1}{2}\cos x\right ) + 3\cos \left (\dfrac {1}{2}\cos x\right )\right )\sin x dx$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.
On the basis of above information answer the following questions