Saturday, 5 December 2015

calculus - Integration of $(5^{3/x}-sqrt[3]{x^8}+9)/(3x^2)$



Problem: evaluate $$\int\frac{5^{3/x}-\sqrt[3]{x^8}+9}{3x^2}\mathrm dx$$




Please provide me a hint. I tried to separate to 3 parts but don't know how to integrate $\frac{5^{3/x}}{3x^2}$.


Answer



Hint: Let $u = \frac{3}{x}$, and then $du = \frac{-3}{x^2} dx$. Then



$$\int \frac{5^{3/x}}{x^2} dx = \int 5^u \frac{du}{-3}$$


No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...