Solve ∫ gamma^3/(x^2+gamma^2)^frac{3{2}}dgamma

$$\int \frac { \gamma ^ { 3 } } { ( x ^ { 2 } + \gamma ^ { 2 } ) ^ { \frac { 3 } { 2 } } } d \gamma$$

Evaluate

$$\frac{-\cos(3\arctan(\frac{\gamma }{|x|}))\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}x^{4}+9|x|\gamma ^{2}x^{4}+4\left(|x|\right)^{3}\gamma ^{4}+9|x|x^{6}}{4\left(|x|\right)^{3}\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}}+С$$

$$x\neq 0$$

Differentiate w.r.t. x

$$\frac{x\left(-27|x|\left(x^{2}+\gamma ^{2}\right)^{\frac{5}{2}}\left(x\gamma \right)^{2}-3\sin(3\arctan(\frac{\gamma }{|x|}))\gamma |x|x^{2}\left(x^{2}+\gamma ^{2}\right)^{3}-4\cos(3\arctan(\frac{\gamma }{|x|}))x^{2}\left(x^{2}+\gamma ^{2}\right)^{4}+36|x|x^{2}\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}\gamma ^{4}+72|x|\gamma ^{2}\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}x^{4}+9\gamma ^{2}\left(|x|\right)^{3}\left(x^{2}+\gamma ^{2}\right)^{\frac{5}{2}}+12|x|\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}\gamma ^{6}+36|x|\left(x^{2}+\gamma ^{2}\right)^{\frac{3}{2}}x^{6}-12|x|\gamma ^{4}\left(x^{2}+\gamma ^{2}\right)^{\frac{5}{2}}-27|x|x^{4}\left(x^{2}+\gamma ^{2}\right)^{\frac{5}{2}}+3\cos(3\arctan(\frac{\gamma }{|x|}))x^{2}\gamma ^{8}+12\cos(3\arctan(\frac{\gamma }{|x|}))x^{4}\gamma ^{6}+12\cos(3\arctan(\frac{\gamma }{|x|}))\gamma ^{2}x^{8}+18\cos(3\arctan(\frac{\gamma }{|x|}))\gamma ^{4}x^{6}+3\cos(3\arctan(\frac{\gamma }{|x|}))x^{10}\right)}{4\left(|x|\right)^{3}\left(x^{2}+\gamma ^{2}\right)^{4}}$$