Question

求定积分，，，

Answer 1

如图

追问

请问倒数第三步怎么来的啊，怎么就分成两项相加了

追答

划横线两个相等

追问

嗯…我有点不明白的地方就是， 第二个式子是第一个式子化出来的啊，为啥还要把他们加起来，

Answer 2

令x=asint，则dx=acostdt
原式=∫(0,π/2) acostdt/(asint+acost)
=∫(0,π/2) costdt/(sint+cost)
=∫(0,π/2) [(sint+cost)+(cost-sint)]/2(sint+cost)dt
=(1/2)*∫(0,π/2) dt+(1/2)*∫(0,π/2) (cost-sint)/(sint+cost)dt
=(1/2)*t|(0,π/2)+(1/2)*∫(0,π/2) d(sint+cost)/(sint+cost)
=π/4+(1/2)*ln|sint+cost||(0,π/2)
=π/4