解決∫ (from 0 to a) of x wrt x/(x^2+z^2)sqrt{2x^2+z^2} |Microsoft數學求解器

$$\int _ { 0 } ^ { a } \frac { x d x } { ( x ^ { 2 } + z ^ { 2 } ) \sqrt { 2 x ^ { 2 } + z ^ { 2 } } }$$

評估

$$\frac{4\arctan(\frac{\sqrt{z^{2}+2a^{2}}}{|z|})-\pi }{4|z|}$$

$$z\neq 0$$

對 z 微分

$$\frac{-\frac{4\left(az\right)^{2}}{\sqrt{z^{2}+2a^{2}}z^{2}}-\frac{4\arctan(\frac{\sqrt{z^{2}+2a^{2}}}{|z|})|z|a^{2}}{z^{2}}-4\arctan(\frac{\sqrt{z^{2}+2a^{2}}}{|z|})|z|+\frac{\pi |z|a^{2}}{z^{2}}+\pi |z|}{4z\left(z^{2}+a^{2}\right)}$$