作业帮图中这道不定积分题是怎么做的?高手来!
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/08/25 09:59:56
图中这道不定积分题是怎么做的?高手来!
像分部积分,但又不是.这是怎么做的?
∫ x/cosx * d(xsinx + cosx)/(xsinx + cosx)²
= x/cosx d[- 1/(xsinx + cosx)]
= - x/cosx * 1/(xsinx + cosx) + ∫ 1/(xsinx + cosx) * (cosx + xsinx)/cos²x dx
= - x/cosx * 1/(xsinx + cosx) + ∫ sec²x dx
= - x/cosx * 1/(xsinx + cosx) + tanx + C
= x/cosx d[- 1/(xsinx + cosx)]
= - x/cosx * 1/(xsinx + cosx) + ∫ 1/(xsinx + cosx) * (cosx + xsinx)/cos²x dx
= - x/cosx * 1/(xsinx + cosx) + ∫ sec²x dx
= - x/cosx * 1/(xsinx + cosx) + tanx + C