∫(上限1,下限0) 2x sinx² + xe^x dx
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∫(上限1,下限0) 2x sinx² + xe^x dx
∫(上限1,下限0) 2x sinx² + xe^x dx
∫(上限1,下限0) 2x sinx² + xe^x dx
∫(0→1) [2xsin(x²) + xe^x] dx
= ∫(0→1) sin(x²) d(x²) + ∫(0→1) x de^x
= - cos(x²)|(0→1) + xe^x|(0→1) - ∫(0→1) e^x dx
= - [cos(1) - cos(0)] + (e - 0) - e^x|(0→1)
= - cos(1) + 1 + e - (e - 1)
= 2 - cos(1)