Math, asked by sharmasweta6574, 7 hours ago

Evaluate
∫2x+1 /x(x+1) dx​

Answers

Answered by abhi569
2

Answer:

   \sf{ln|x + 1| + ln |x|\: + C}

Step-by-step explanation:

 \int \frac{2x + 1}{x(x + 1)} dx \\  \\  \int \frac{x + ( x + 1) }{x(x + 1)} dx \\  \\  \int \frac{x}{x(x + 1)} dx +  \int \frac{(x + 1)}{ x(x + 1)} dx \\  \\  \int \frac{1}{x + 1} dx +  \int \frac{1}{x} dx \\  \\  \sf{ln|x + 1| + ln |x|\: + C }

Integration of f(ax + b) is F(ax + b)/a, as happened in integration of 1/(x + 1).

Int. of 1/(x + 1) = ln|x + 1|/1 = ln|x + 1|

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