Question

∫(³√x-(1÷√x)+1)dx算不定积分 ∫(sinx-3e^x+(2÷√(1-x²)dx

Answer 1

(1)
∫ [ x^(1/3) - 1/x + 1 ] dx
=(3/4)x^(4/3) - ln|x| + x + C
(2)
∫[sinx-3e^x+ 2/√(1-x^2) ]dx
=-cosx - 3e^x + 2arcsinx + C

追问

(2)的过程能写一下吗?看不懂

(2)的过程能写一下吗?看不懂

追答

(2)
∫sinx dx =-cosx + C1
∫e^x dx + e^x + C2
∫dx/√(1-x^2) = arcsinx + C3
∫[sinx-3e^x+ 2/√(1-x^2) ]dx
=∫sinx dx-3∫e^x dx+ 2∫ dx/√(1-x^2)
=-cosx - 3e^x + 2arcsinx + C