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Question
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Options
10x - x10 + C
10x + x10 + C
(10x - x10)-1 + C
log (10x + x10) + C
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Solution
log (10x + x10) + C
Explanation:
Let `I = int (10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx`
Put x10 + 10x = t
(10x9 + 10x loge 10) dx = dt
`therefore I = int dt/d`
= log |t| + C
= log (10x + x10) + C
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