Integral of x/(y^2+x^2) dy
The solution
Detail solution
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The integral of a constant times a function is the constant times the integral of the function:
∫x2+y2xdy=x∫x2+y21dy
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The integral of y2+11 is x2atan(x2y).
So, the result is: x2xatan(x2y)
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Add the constant of integration:
x2xatan(x2y)+constant
The answer is:
x2xatan(x2y)+constant
The answer (Indefinite)
[src]
/ y \
x*atan|-------|
/ | ____|
| | / 2 |
| x \\/ x /
| ------- dy = C + ---------------
| 2 2 ____
| y + x / 2
| \/ x
/
∫x2+y2xdy=C+x2xatan(x2y)
I*log(-I*x) I*log(1 + I*x) I*log(I*x) I*log(1 - I*x)
----------- + -------------- - ---------- - --------------
2 2 2 2
2ilog(−ix)−2ilog(ix)−2ilog(−ix+1)+2ilog(ix+1)
=
I*log(-I*x) I*log(1 + I*x) I*log(I*x) I*log(1 - I*x)
----------- + -------------- - ---------- - --------------
2 2 2 2
2ilog(−ix)−2ilog(ix)−2ilog(−ix+1)+2ilog(ix+1)
i*log(-i*x)/2 + i*log(1 + i*x)/2 - i*log(i*x)/2 - i*log(1 - i*x)/2
Use the examples entering the upper and lower limits of integration.