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Evaluate: int(10x^9+10^x(log)e 10)/(10^x...

Evaluate: `int(10x^9+10^x(log)_e 10)/(10^x+x^(10))dx`

A

`10^(x)-x^(10)+C`

B

`10^(x)+x^(10)+C`

C

`10^(x)-(x^(10)-x^(-1))+C`

D

`log|10^(x)+x^(10)|+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`int((10x^(9)+10^(x)log_(e)10)/(x^(10)+10^(x)))dx`
Let`" "x^(10)+10^(x)=t`
`rArr (10x^(9)+10^(x)log_(e)10)dx=dt`
`=int(dt)/(t)=log|t|+Clog|10^(x)+x^(10)|+C`
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