Mathematics

# $\int {{3^x}{3^{{3^x}}}{3^{{3^{{3^x}}}}}} dx$ is equal to

$\dfrac{{{3^{{3^{{3^x}}}}}}}{{{{\left( {\log 3} \right)}^3}}} + C$

##### SOLUTION
$I\displaystyle\int 3^x3^{3^x}3^{3^{3^x}}dx$

put $3^x=p$

$3^xlog 3dx=dp$
$\Rightarrow I=\dfrac{1}{log 3}\displaystyle\int 3^p3^{3^p}dp$

put $3^p=k$

$3^plog 3dp=dk$
$I=\dfrac{1}{(log 3)^2}\displaystyle\int 3^kdk$
$\Rightarrow I=\dfrac{1}{(log 3)^3}3^k$

$=\dfrac{1}{(log 3)^3}3^{3^p}=\dfrac{1}{(log 3)^3}3^{3^{3^x}}$

$\therefore \displaystyle\int 3^x3^{3^x}3^{3^{3^x}}dx=\dfrac{1}{(log3)^3}3^{3^{3^x}}+c$.

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Integrate:

$\displaystyle \int \dfrac{{1 - x}}{{2{x^2} + 1}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Multiple Correct Medium
If $\displaystyle \int x^{2}e^{-2x}dx=e^{-2x}(ax^{2}+bx+c)+d$ then
• A. $b=2$
• B. $a=-\displaystyle \frac {1}{2}$
• C. $c=-\displaystyle \frac{1}{4}$
• D. $d\in R$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\int \left( {7x - 2} \right)\,\sqrt {3x + 2} \,dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int_{0}^{\pi /2}\frac{dx}{\sin x}$equals
• A. $\displaystyle \frac{1}{2}$
• B. $1$
• C. $3/2$
• D. $0$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$