Integral of ln(y) dx
The solution
Detail solution
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Use integration by parts:
∫udv=uv−∫vdu
Let u(y)=log(y) and let dv(y)=1.
Then du(y)=y1.
To find v(y):
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The integral of a constant is the constant times the variable of integration:
∫1dy=y
Now evaluate the sub-integral.
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The integral of a constant is the constant times the variable of integration:
∫1dy=y
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Now simplify:
y(log(y)−1)
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Add the constant of integration:
y(log(y)−1)+constant
The answer is:
y(log(y)−1)+constant
The answer (Indefinite)
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| log(y) dy = C - y + y*log(y)
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∫log(y)dy=C+ylog(y)−y
The graph
Use the examples entering the upper and lower limits of integration.