Evaluating Integrals

[clmason]

I missed a class right before my spring break, and I am finding myself a little behind on the material. There are two questions I have on an assignment that I am working on right now.

1) Evaluate the following:
integral ln(x) / sqrt(x) dx

and

2) Using the reduction formula integral cos^n(x) dx= 1/n cos^n-1 (x) sin (x) + (n-1)/n integral cos^n-2 (x) dx evaluate:
a) integral cos^4 (x) dx

Thanks for any help,

-CM

 

[royhaas]

Use \(\displaystyle y=\ln(x)\) for the 1st problem. For the second, write \(\displaystyle \cos^2(x)\) in terms of \(\displaystyle \cos(2x)\).

 

[BigGlenntheHeavy]

For 1 use integration by parts, let u = ln(x) and dv = dx/x^(1/2).

Ans. 2x^(1/2)[ln(x)-2]+c.