+0  
 
0
318
2
avatar+227 

I get integrals and indefinite integrals. I do. I just don't get this one: 

$$\int\frac{e^{sqrt(x)}}{sqrt(x)}$$

By the way, I couldn't figure out how to get square roots using LaTeX, so sqrt is square root.

Any help, please???

ThisGuy  Feb 24, 2015

Best Answer 

 #1
avatar+26640 
+10

1. Use \sqrt{x} to get  $$\sqrt{x}$$

 

2. Use the substitution:

 $$u=\sqrt{x}$$

 

$$\\du=\frac{dx}{2\sqrt{x}}\\2\sqrt{x}du=dx\\2udu=dx$$

 

So:

$$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}dx=\int \frac{e^{u} \times 2udu}{u}$$

 

or:

$$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}dx=2\int e^{u}du = 2e^u=2e^{\sqrt{x}}$$

.

Alan  Feb 24, 2015
Sort: 

2+0 Answers

 #1
avatar+26640 
+10
Best Answer

1. Use \sqrt{x} to get  $$\sqrt{x}$$

 

2. Use the substitution:

 $$u=\sqrt{x}$$

 

$$\\du=\frac{dx}{2\sqrt{x}}\\2\sqrt{x}du=dx\\2udu=dx$$

 

So:

$$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}dx=\int \frac{e^{u} \times 2udu}{u}$$

 

or:

$$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}dx=2\int e^{u}du = 2e^u=2e^{\sqrt{x}}$$

.

Alan  Feb 24, 2015
 #2
avatar+227 
+5

Ugh, now this seems way too simple. Thank you a ton!

ThisGuy  Feb 24, 2015

6 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details