Mathematics

# Write a value of $\int { { e }^{ 2{ x }^{ 2 }+\ln { x } } } dx$

##### SOLUTION
$I=\displaystyle\int{{e}^{2{x}^{2}+\ln{x}}dx}$

$=\displaystyle\int{{e}^{2{x}^{2}}{e}^{\ln{x}}dx}$

$=\displaystyle\int{{e}^{2{x}^{2}}x\,dx}$

Let $t={x}^{2}\Rightarrow\,dt=2x\,dx$

$=\displaystyle\int{{e}^{2t}dt}$

$=\dfrac{{e}^{2t}}{2}+c$

$=\dfrac{{e}^{2{x}^{2}}}{2}+c$    .....where $t={x}^{2}$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
$\int _{ 0 }^{ \pi }{ x\log { \sin { xdx } } }$ is equal to
• A. $-\dfrac { 1 }{ 2 } \log { \dfrac { 1 }{ 2 } }$
• B. $-\dfrac { {\pi}^{2} }{ 2 } \log { \dfrac { 1 }{ 2 } }$
• C. $-\dfrac { \pi }{ 2 } \log { 2 }$
• D. $-\dfrac { \pi }{ 2 } \log { \dfrac { 1 }{ 2 } }$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\int x^{x^2 +1} (2 \ln x + 1) dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int \frac{1}{x\log x\log \left ( \log x \right )}dx.$
• A. $\displaystyle \left [ \log \left ( \log x \right ) \right ].$
• B. $\displaystyle \log \left [ \log \left ( \log x^{2} \right ) \right ].$
• C. $\displaystyle -\log \left [ \log \left ( \log x \right ) \right ].$
• D. $\displaystyle \log \left [ \log \left ( \log x \right ) \right ].$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate $\displaystyle\int_{4}^{9}\dfrac{\sqrt{x}}{(30-x^{3/2})^{2}}\ dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
Integrate the Rational Function $\displaystyle\int {\dfrac{{2x}}{{x\left( {{x^2} + 1} \right)}}}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020