Definite Integral

[abilitiesz]

Hello,

I need some help on my calculus homework. I've tried each problem roughly 10-20 times, but I keep getting the wrong answer. Any help is appreciated. Thank you.

 

[tkhunny]

Are you actually sitting in the exam right now?

These are textbook examples of "Substitution".

Hints:
\(\displaystyle \frac{d}{dx} \ln(x) = \frac{1}{x}\)

\(\displaystyle \frac{d}{dx} x^{5} = 5x^{4}\)

Now, go to! Harvest the field of integrals before it is past the time for reaping!!

 

[abilitiesz]

Oh, no. I'm not sitting in an exam lol. I'm at home trying to do hw. I hate internet assignments. :? You have to enter it in perfectly otherwise the system wont see it as a correct answer. It's a pain. Thank you for the advice. I'll try it out now and see if I can get the results.

 

[abilitiesz]

Hey, I still can't figure it out. =/ can you give me any more hints?

 

[galactus]

\(\displaystyle \int x^{4}cos(x^{5})dx\)

Let \(\displaystyle u=x^{5}, \;\ du=5x^{4}dx\)

Now, see it?. The sub is rather easy and turns it into an easy integral.

\(\displaystyle \int\frac{1}{x\sqrt{ln(x)}}dx\)

Let \(\displaystyle u=ln(x), \;\ du=\frac{1}{x}dx\)

 

[BigGlenntheHeavy]

\(\displaystyle \int_{e}^{e^9} \frac{dx}{x\sqrt ln|x|} \ Let \ u \ = \ ln|x|, \ then \ du \ = \ \frac{1}{x}dx\)

\(\displaystyle Ergo, we \ have \ \int_{1}^{9} \frac{du}{u^{1/2}} \ = \ 2u^{1/2}\bigg]_{1}^{9} \ = \ 4.\)