Solve -t^2sqrt{t^2+1}+2/3(t^2+1)^frac{3{2}}+c

$$- t ^ { 2 } \sqrt { t ^ { 2 } + 1 } + \frac { 2 } { 3 } ( t ^ { 2 } + 1 ) ^ { \frac { 3 } { 2 } } + c$$

Factor

$$\frac{-3\sqrt{t^{2}+1}t^{2}+2\left(t^{2}+1\right)^{\frac{3}{2}}+3c}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{-3t^{2}\sqrt{t^{2}+1}+2\left(t^{2}+1\right)^{\frac{3}{2}}+3c}{3}$$

Evaluate

$$-\sqrt{t^{2}+1}t^{2}+\frac{2\left(t^{2}+1\right)^{\frac{3}{2}}}{3}+c$$