Calculus Problems

bhav

Hi Everybody
I am new to this forum and thanks fo having me. I am still learning the rules for posting and will try not to infinge on any of the rules.
I am having a problem solving the ffg. 2 problems and would really like some assistance.

1.Find dy/dx if $$\displaystyle y=(sqrt x^2(1-sqrt x)/(1+sqrt x))$$

2. Find integral of $$\displaystyle dx/x(sqrt 4-(3lnx)^2)$$

Thanks in advance for all the assistance

Prove It

MHF Helper
This is very hard to read.

Are these what you were trying to write?

1. Find $$\displaystyle \frac{dy}{dx}$$ if $$\displaystyle y = \frac{\sqrt{x^2(1 - \sqrt{x})}}{1 + \sqrt{x}}$$?

2. Find $$\displaystyle \int{\frac{dx}{x\sqrt{4 - (3\ln{x})^2}}}$$?

For 2.

$$\displaystyle \int{\frac{dx}{x\sqrt{4 - (3\ln{x})^2}}} = \frac{1}{3}\int{\left(\frac{1}{\sqrt{4 - (3\ln{x})^2}}\right)\left(\frac{3}{x}\right)\,dx}$$.

Now let $$\displaystyle u = 3\ln{x}$$ so that $$\displaystyle du = \frac{3}{x}\,dx$$ and the integral becomes

$$\displaystyle \frac{1}{3}\int{\frac{1}{\sqrt{4 - u^2}}\,du}$$.

Now try a substitution of $$\displaystyle u = 2\sin{\theta}$$ so that $$\displaystyle du = 2\cos{\theta}\,d\theta$$.