Mathematics

# Solve :$\int e^{x^2+\text{ln x}} . dx$

##### SOLUTION
We have,
$I=\int e^{x^2+ln\ x} dx$
$I=\int e^{x^2}. e^{ln\ x} dx$
$I=\int e^{x^2}. x dx$

Let $t=x^2$
$dt=2xdx$

Therefore,
$I=\dfrac{1}{2}\int e^{t}dt$
$I=\dfrac{1}{2}e^t+C$

On putting the value of $t$, we get
$I=\dfrac{1}{2}e^{x^2}+C$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
Find the derivative of $\dfrac{e^{x}}{\sin x}$.
• A. $e^x\text{cosec }x[\cot x+1]$
• B. $e^x\sec x[\cot x+1]$
• C. $e^x\sec x[\cot x-1]$
• D. $e^x\text{cosec }x[1-\cot x]$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate:
$\displaystyle\int_{0}^{\pi/4}\dfrac{\tan^{3}x}{1+\cos 2x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 One Word Medium
Solve $\displaystyle \int_{0}^{\pi /2}\frac{\cos x-\sin x}{1+\sin x\cos x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate $\displaystyle \int_{0}^{\pi} \dfrac{x \sin \ x}{1 + \sin \ x}dx$

$\int \dfrac{a^x}{\sqrt{1-a^{2x}}}dx$