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<html><div class="math">\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, I n u_{0} \int_{R_{1}}^{R_{2}} y^{2} \int_{-\frac{1}{2} \, a}^{\frac{1}{2} \, a} \frac{1}{{\left({\left(L - r + x\right)}^{2} + y^{2}\right)}^{\frac{2}{3
,{d x}\,{d y} + \frac{1}{2} \, I n u_{0} \int_{R_{1}}^{R_{2}} y^{2} \int_{-\frac{1}{2} \, a}^{\frac{1}{2} \, a} \frac{1}{{\left({\left(r - x\right)}^{2} + y^{2}\right)}^{\frac{2}{3}}}\,{d x}\,{d y}
}}}
B1为上面积分式中第一个二重积分.
B1对x的积分结果B11为:B1为上面积分式中第一个二重积分.
B1对x的积分结果B11为:
<html><div class="math">\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, {\left(\frac{{\left(a - 2 \, r\right)} \sqrt{a^{2} - 4 \, a r + 4 \, r^{2} + 4 \, y^{2
4 \, y^{4} + {\left(a^{2} - 4 \, a r + 4 \, r^{2}\right)} y^{2}} + \frac{{\left(a + 2 \, r\right)} \sqrt{a^{2} + 4 \, a r + 4 \, r^{2} + 4 \, y^{2}}}{4 \, y^{4} + {\left(a^{2} + 4 \, a r + 4 \, r^{2}\right)} y^{2}}\right)} I n u_{0} y^{2}
B1对x积分后的结果B11对y积分,就无法积分出结果:
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, I n u_{0} \int_{R_{1}}^{R_{2}} {\left(\frac{{\left(a - 2 \, r\right)} \sqrt{a^{2} - 4 \, a r + 4 \, r^{2} + 4 \, y^{2}}}{4 \, y^{4} + {\left(a^{2} - 4 \, a r + 4 \, r^{2}\right)} y^{2}} + \frac{{\left(a + 2 \, r\right)} \sqrt{a^{2} + 4 \, a r + 4 \, r^{2} + 4 \, y^{2}}}{4 \, y^{4} + {\left(a^{2} + 4 \, a r + 4 \, r^{2}\right)} y^{2}}\right)} y^{2}\,{d y}
如果对B11前半部分单独积分,仍不能积分出结果:
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(a - 2 \, r\right)} \int_{R_{1}}^{R_{2}} \frac{\sqrt{a^{2} - 4 \, a r + 4 \, r^{2} + 4 \, y^{2}} y^{2}}{4 \, y^{4} + {\left(a^{2} - 4 \, a r + 4 \, r^{2}\right)} y^{2}}\,{d y}
}}}