Question

20dx" id="TexFormula1" title="\int\limits^8_2 {\frac{\sqrt{x^2+64} }{2x^2} } \, dx" alt="\int\limits^8_2 {\frac{\sqrt{x^2+64} }{2x^2} } \, dx" align="absmiddle" class="latex-formula">Don't get how to do this problem. Plz help!

Answer 1

Answer:

Step-by-step explanation:

$\int\limits^8_2 {\frac{1}{\sqrt{x^2+64} } } \, dx$

$u= x/8 \rightarrow dx = 8 du$

$x^2 = 64 u\rightarrow x^2+64 = 64 u^2 + 64 = 64 ( u^2 +1)$

$\int\limits^1_{1/4} {\frac{1}{8\sqrt{u^2+1} } } \, 8du$

$\int\limits^1_{1/4} {\frac{1}{\sqrt{u^2+1} } \, du$

$=ln(\sqrt{u^2+1}+u|_{1/4} ^1$