`int(10x^(9)+10^(x)log_(e)10dx)/(x^(10)+10^(x))` बराबर है :

Options

A. `10^(x)-x^(10)+C`
B. `10^(x)+x^(10)+C`
C. `(10^(x)-x^(10))^(-1)+C`
D. `log(10^(x)+x^(10))+C`

Answer

D

Explanation

`int[(10x^(9)+10^(x)loge^(10))/(x^(10)+10^(x))]dx" "{:(" माना "x^(10)+10^(x)=t),(rArr(10x^(9)+10^(x)log_(e)10)),(" "dx=dt):}`
`=int(1)/(t)dt=log|t|+c`
`=log|x^(10)+10^()|+c`