Question

对(X除以x平方加y平方的和)x积分

Answer 1

∫(x/(x²+y²))dx

令t=x²+y²

dt/dx=2x

2xdx=dt

∫(x/(x²+y²))dx

=(1/2)∫(1/(x²+y²))(2xdx)

=(1/2)∫(1/t)dt

=(1/2)ln|t| + C

=(1/2)ln(x²+y²) + C