∫(x+x³)/(1+(x²)²)dx的具体解答
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 03:47:18
![∫(x+x³)/(1+(x²)²)dx的具体解答](/uploads/image/z/1024662-30-2.jpg?t=%E2%88%AB%28x%2Bx%26%23179%3B%EF%BC%89%2F%281%2B%28x%26%23178%3B%29%26%23178%3B%29dx%E7%9A%84%E5%85%B7%E4%BD%93%E8%A7%A3%E7%AD%94)
∫(x+x³)/(1+(x²)²)dx的具体解答
∫(x+x³)/(1+(x²)²)dx的具体解答
∫(x+x³)/(1+(x²)²)dx的具体解答
原积分
=0.5 *∫ (1+x²) / [1+(x²)²] d(x²)
=0.5 *∫ 1/ [1+(x²)²] d(x²) + 0.5 *∫ x² /[1+(x²)²] d(x²)
=0.5arctanx² + ∫ 0.25 /[1+(x²)²] d(x²)²
=0.5arctanx² + 0.25 *ln[1+(x²)²] +C,C为常数