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

More "M.C.Q (1 Marks)" from STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\tan ({\cos ^{ - 1}}x)$ is equal to

Find the value of $x,$ if $\begin{bmatrix}2&5\\3&\text{x}\end{bmatrix}=\begin{bmatrix}\text{x}&-1\\5&3\end{bmatrix}$ is:

The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x + y - z =0= x -2 y +3 z -5$ is.

Let $f$ and $g$ are twice differentiable functions such that $f(x).g(x) = 1\,\, \forall x \in R$ and $f'$ and $g'$ are never zero, then $\frac{{f^{''}(x)}}{{f(x)}} + \frac{{g^{''}(x)}}{{g(x)}}$ equals-

Consider the following statements:Statement $I:\ $ The area bounded by the curve, $\text{y}=\sin\text{x}$ between $\text{x}=0$ and $x = 2p$ is $2\ sq.$ units.Statement $II:\ $ The area bounded by the curve, $\text{y}=2\cos\text{x}$ and the $x-$axis from $\text{x}=0$ to $x = 2p$ is $8\ sq.$ units.

If $y = \sin \left( {{{1 + {x^2}} \over {1 - {x^2}}}} \right)$, then ${{dy} \over {dx}} = $

The vector in the direction of the vector $\hat{i}-2 \hat{j}+2 \hat{k}$ that has magnitude 9 is

Evaluate: $\int\frac{3\text{x}^2+1}{(\text{x}^2-1)^3}\text{dx}$

Let $F(x)=\int_x^{x^2+\frac{\pi}{6}} 2 \cos ^2 t d t$ for all $x \in R$ and $f:\left[0, \frac{1}{2}\right] \rightarrow[0, \infty)$ be a continuous function. For $a \in\left[0, \frac{1}{2}\right]$, if $F^{\prime}(a)+2$ is the area of the region bounded by $x=0, y=0, y=f(x)$ and $x=a$, then $f(0)$ is

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = $