Mathematics

# If $\displaystyle\int 2^{2x}\cdot 2^xdx=A\cdot 2^{2^x}+c$, then $A=?$

$\dfrac{1}{(log 2)^2}$

##### SOLUTION
$2^x=z\Rightarrow 2^xdx=\dfrac{dz}{ln 2}$

$\Rightarrow \dfrac{1}{ln 2}\displaystyle\int 2^zdz=\dfrac{1}{(ln 2)^2}2^{2^x}+c$.

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

#### Realted Questions

Q1 Subjective Medium
Solve:
$\int {\dfrac{x}{{{x^4} - {x^2} + 1}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
if $\displaystyle f(x)=\frac{e^x}{1+e^x},I_1=\int_{ f(-a) }^{f(a)}xg(x(1-x))\:dx$, and $\displaystyle I_2=\int_{ f(-a) }^{f(a)}g(x(1-x))\:dx$,then the value of $\dfrac{I_2}{I_1}$ is
• A. $-1$
• B. $-2$
• C. $1$
• D. $2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $l_{n}=\displaystyle \int{\dfrac{t^{n}}{1+t^{2}}}dt$ then
• A. $l_{n+1}=\dfrac{t^{n+1}}{n+1}l_{n}$
• B. $l_{n+1}=\dfrac{t^{n-1}}{n-1}l_{n}$
• C. $l_{n21}=\dfrac{t^{n+1}}{n+1}l_{n}$
• D. $l_{n+2}=\dfrac{t^{n}}{n}-nl_{n}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\int \int_{R} e^{-(x^{2} + y^{2})}dx dy$, where $R$ is the region bounded by the circle $x^{2} + y^{2} = a^{2}$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
If the value of the integral $\displaystyle \int_{1}^{2}e^{x^{2}}dx$ is $\displaystyle a$, then the value of $\displaystyle \int_{e}^{e^{4}}\sqrt{lnx}dx$ is
• A. $\displaystyle e^{4}-e-\alpha$
• B. $\displaystyle 2\left ( e^{4}-e \right )-\alpha$
• C. $\displaystyle 2e^{4}-1-\alpha$
• D. $\displaystyle2e^{4}-e-\alpha$