∫ (cos√x)/√x dx
= 2∫ cos(√x) d√x
= 2sin(√x) + C
∫ [√x + 2x²/(1 + x²) - cos3x] dx
= ∫ √x dx + 2∫ [(x² + 1) - 1]/(1 + x²) dx - ∫ cos3x dx
= ∫ √x dx + 2∫ [1 - 1/(1 + x²)] dx - (1/3)∫ cos3x d(3x)
= (2/3)x^(3/2) + 2x - 2arctan(x) - (1/3)sin(3x) + C,公式∫ 1/(1 + x²) dx = arctan(x) + C
∫ [1/√x + 2x²/(1 + x²) - e^(2x)] dx
= ∫ 1/√x dx + 2∫ [(x² + 1) - 1]/(1 + x²) - ∫ e^(2x) dx
= ∫ 1/√x dx + 2∫ [1 - 1/(1 + x²)] dx - (1/2)∫ e^(2x) d(2x)
= 2√x + 2x - 2arctan(x) - (1/2)e^(2x) + C
您的支持就是我们的动力.
