Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Choose the correct answer in Exercise:
$\int\frac{\text{dx}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}$ is equal to
  • ✓
    $\tan^{-1}(\text{e}^{\text{x}})+\text{C}$
  • B
    $\tan^{-1}\text{(e}^{\text{x}})+\text{C}$
  • C
    $\log(\text{e}^{\text{x}}-\text{e}^{\text{x}})+\text{C}$
  • D
    $\log(\text{e}^{\text{x}}+\text{e}^\text{x})+\text{C}$
✓

Answer

Correct option: A.
$\tan^{-1}(\text{e}^{\text{x}})+\text{C}$
$\text{Let I}=\int\frac{\text{dx}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}\text{dx}=\int\frac{\text{e}^{\text{x}}}{\text{e}^{2\text{x}}+1}\text{dx}$

Also, let $\text{e}^{\text{x}}=\text{t}\Rightarrow\text{e}^{\text{x}}\ \text{dx}=\text{dt}$

$\therefore\text{I}=\int\frac{\text{dt}}{1+\text{t}^{2}}$

$=\tan^{-1}\text{t}+\text{C}$

$=\tan^{-1}\text{(e}^{\text{x}})+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $x, y, z$ are different from zero and $\begin{vmatrix}1+\text{x}&1&1\\1&1+\text{y}&1\\1&1&1+\text{z}\end{vmatrix}=0,$ then the value $x^{-1} + y^{-1} + z^{-1}$ is:
→
The value of the cofactor of the element of second row and third column in the matrix $\left[\begin{array}{ccc}4 & 3 & 2 \\ 2 & -1 & 0 \\ 1 & 2 & 3\end{array}\right]$ is:
→
If $2f(sinx) + f(cos x) = x,$ then $\frac{d}{{dx}}$ $f(x)$ is
→
If $\vec p$ and $\vec q$ are unequal unit vectors such that $\left( {\vec p - \vec q} \right) . \left( {\left( {2\vec q + \vec p} \right) \times \left( {3\vec p - \vec q} \right)} \right) = \left| {\vec p + \vec q} \right|$ , then angle between $\vec p$ and $\vec q$ will be
→
For a sufficiently large value of $n$ the sum of the square roots of the first $n$ positive integers i.e.$\sqrt 1  + \sqrt 2  + \sqrt 3  + ...................... + \sqrt n$ is approximately equal to
→
A straight line passes through $(1, -2, 3)$ and perpendicular to the plane $2x + 3y - z = 7.$ Find the direction ratios of normal to plane:
→
The area of the region bounded by $y = (x - 4)^2, y = 16 - x^2 $ and the $x$ axis, is:
→
Consider the function $f (x) = x^3 - 8x^2 + 20x -13$
The function $f (x)$ defined for $R \rightarrow R$
→
If $f(x) = \frac{x}{{1 + x}}$, then ${f^{ - 1}}(x)$ is equal to
→
Two dice $A$ and $B$ are rolled, Let the numbers obtained on $A$ and $B$ be $\alpha$ and $\beta$ respectively. If the variance of $\alpha-\beta$ is $\frac{p}{q}$, where $p$ and $q$ are coprime, then the sum of the positive divisors of $p$ is equal to
→