∫负无穷到正无穷1/x^2+2x+2dx

优质解答

∫负无穷到正无穷1/（x^2+2x+2）dx
=∫负无穷到正无穷1/[（x+1）^2+1]dx
=∫负无穷到正无穷1/1/[（x+1）^2+1]d（x+1）
=arctan(x+1）│负无穷到正无穷
=π/2-（-π/2）
=π ∫负无穷到正无穷1/（x^2+2x+2）dx
=∫负无穷到正无穷1/[（x+1）^2+1]dx
=∫负无穷到正无穷1/1/[（x+1）^2+1]d（x+1）
=arctan(x+1）│负无穷到正无穷
=π/2-（-π/2）
=π