Solve x ^ 2 / 2 left( sinh ( x ) right) ^ -1 - 1 / 2 ∫ sqrt{ 1+ x ^ 2 } wrt x

$$\frac{ { x }^{ 2 } }{ 2 } { \left( \sinh ( x ) \right) }^{ -1 } - \frac{ 1 }{ 2 } \int{ \sqrt{ 1+ { x }^{ 2 } } }d x$$

Factor

$$\frac{\frac{2x^{2}}{\sinh(x)}-\ln(|\sqrt{x^{2}+1}+x|)-x\sqrt{x^{2}+1}-2С}{4}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\frac{x^{2}}{\sinh(x)}-\int \sqrt{1+x^{2}}\mathrm{d}x}{2}$$

Evaluate

$$\frac{x^{2}}{2\sinh(x)}-\frac{\ln(|\sqrt{x^{2}+1}+x|)}{4}-\frac{x\sqrt{x^{2}+1}}{4}-\frac{С}{2}$$