Solve 1/2log_{e}({left|x^2+1right|})-3left(x^2+1right)^2/8{left(x^2+1right)^frac{3{2}}}

$$\frac{ 1 }{ 2 } \log_{ e }({ \left| { x }^{ 2 } +1 \right| }) - \frac{ 3 { \left( { x }^{ 2 } +1 \right) }^{ 2 } }{ 8 { \left( { x }^{ 2 } +1 \right) }^{ \frac{ 3 }{ 2 } } }$$

Factor

$$\frac{4\ln(x^{2}+1)-3\sqrt{x^{2}+1}}{8}$$

Solution Steps

Cancel out \left(x^{2}+1\right)^{\frac{3}{2}} in both numerator and denominator.

$$factor(\frac{1}{2}\log_{e}\left(|x^{2}+1|\right)-\frac{3\sqrt{x^{2}+1}}{8})$$

Factor out \frac{1}{8}.

$$\frac{4\log_{e}\left(x^{2}+1\right)-3\sqrt{x^{2}+1}}{8}$$

Evaluate

$$\frac{\ln(x^{2}+1)}{2}-\frac{3\sqrt{x^{2}+1}}{8}$$