\int\limits^8_2 {(√(x^2+64) )/(2x^2) } \, dxDon't get how to do this problem. Plz help!

Question

`\int\limits^8_2 {(√(x^2+64) )/(2x^2) } \, dx`Don't get how to do this problem. Plz help!

Answer 1

Explanation:

`\int\limits^8_2 {(1)/(√(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) {(1)/(8√(u^2+1) ) } \, 8du`

`\int\limits^1_(1/4) {(1)/(√(u^2+1) ) \, du`

`=ln(√(u^2+1)+u|_(1/4) ^1`