If c is any arbitrary constant, then 2^ 2^ 2^x 2^ 2^x 2^x dx is e… - Vidyadip

MCQ

If $c$ is any arbitrary constant, then $\int {{2^{{2^{{2^x}}}}}{2^{{2^x}}}{2^x}dx} $ is equal to

A
$\frac{{{2^{{2^x}}}}}{{{{(\ln 2)}^3}}} + c$
✓
$\frac{{{2^{{2^{{2^x}}}}}}}{{{{(\ln 2)}^3}}} + c$
C
${2^{{2^{{2^x}}}}}{(\ln 2)^3} + c$
D
None of these

✓

Answer

Correct option: B.

$\frac{{{2^{{2^{{2^x}}}}}}}{{{{(\ln 2)}^3}}} + c$

b
(b) Putting ${2^{{2^{{2^x}}}}} = t \Rightarrow {2^{{2^{{2^x}}}}}{2^{{2^x}}}{2^x}{(\log 2)^3}dx = dt,$ we get
$\int_{}^{} {{2^{{2^{{2^x}}}}}{{.2}^{{2^x}}}{{.2}^x}dx} = \frac{1}{{{{(\log 2)}^3}}}\int_{}^{} {1\,.\,dt} = \frac{t}{{{{(\log 2)}^3}}} + c$
$ = \frac{{{2^{{2^{{2^x}}}}}}}{{{{(\log 2)}^3}}} + 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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\mathop {\lim }\limits_{x \to \infty } $ $\frac{{({e^{\mu x}} + 5)}}{{({e^{100x}} + 7)}}$ exists, then sum of all possible positive integral values of $\mu $ is -

The locus of the points $z$ which satisfy the condition arg $\left( {\frac{{z - 1}}{{z + 1}}} \right)$ =$\frac{\pi }{3}$ is

If the function $f(x)=\left(\frac{1}{x}\right)^{2 x} ; x>0$ attains the maximum value at $x =\frac{1}{ e }$ then :

$y = \frac{x}{{x + 1}}$ is a solution of the differential equation

Let $f :R \to R$ be a function defined as $f\left( x \right) = \left\{ \begin{array}{l}5,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\\ a + bx,\,\,\,\,if\,\,\,\,\,\,1 < x < 3\\ b + 5x,\,\,\,\,if\,\,\,\,\,\,3 \le x < 5\\ 30,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \ge 5 \end{array} \right.\,\,\,\,$ Then $f$ is

Let $y=y(x)$ be solution of the differential equation $\log _{e}\left(\frac{d y}{d x}\right)=3 x+4 y$, with $y(0)=0$. If $y\left(-\frac{2}{3} \log _{e} 2\right)=\alpha \log _{e} 2$, then the value of $\alpha$ is equal to:

$\mathop {\lim }\limits_{x \to 1} {\left( {\frac{4}{\pi }{{\tan }^{ - 1}}x} \right)^{\frac{1}{{({x^2} - 1)}}}}$ is equal to -

If $A = \left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\a&b&{ - 1}\end{array}} \right]$, then ${A^2} = $

Let $A =\{1,2,3, \ldots, 10\}$ and $f: A \rightarrow A$ be defined as $f( k )=\left\{\begin{array}{cl} k +1 & \text { if } k \text { is odd } \\ k & \text { if } k \text { is even }\end{array}\right.$

Then the number of possible functions $g : A \rightarrow A$ such that $gof=f$ is ...... .

If the line $y = 2x + k$ is a tangent to the curve ${x^2} = 4y$, then $k$ is equal to