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∫(1+x)/(1+9x^2)dx
题目详情
∫(1+x)/(1+9x^2) dx
▼优质解答
答案和解析
∫ (1+x)/(1+9x^2) dx = ∫ [1/(1+9x^2)] dx + ∫ [x/(1+9x^2)] dx
= (1/3) ∫ [1/(1+9x^2)] d(3x) + (1/18) ∫ [1/(1+9x^2)] d(1+9x^2)
= (1/3) arctan(3x) + (1/18)ln(1+9x^2)+C
= (1/3) ∫ [1/(1+9x^2)] d(3x) + (1/18) ∫ [1/(1+9x^2)] d(1+9x^2)
= (1/3) arctan(3x) + (1/18)ln(1+9x^2)+C
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