Question

`sqrt((10x^9 + 10^x  log e^10)/(x^10 + 10^x)) dx` equals

Options

• `10^x - x^10 + c`

• `10^v + x^10 + c`

• `(10^x - x^10)^-1 + c`

• `log (10^x + x^10) + c`

Answer 1

`log (10^x + x^10) + c`

Explanation:

`sqrt((10x^9 + 10^x  log e^10)/(x^10 + 10^x)) dx` put `x^10 + 10^x = t`

∴ `(10x^9 + 10^x loge10) dx = dt`

= `int (dt)/t = log|t|tc = log|x^10 + 10^x| + c`