Løs ∫ (from 0 to log ( 1 + sqrt { 2) of )}(frac{e^{x}-e^{-x}}{2})^3(e^x-e^-x/2)^1/1d

$$\int _ { 0 } ^ { \log ( 1 + \sqrt { 2 } ) } ( \frac { e ^ { x } - e ^ { - x } } { 2 } ) ^ { 3 } ( \frac { e ^ { x } - e ^ { - x } } { 2 } ) ^ { 1 / 1 } d$$

Evaluer

$$\frac{\left(\sqrt{2}+1\right)^{4\log(e)}d}{64}-\frac{\left(\sqrt{2}+1\right)^{2\log(e)}d}{8}+\frac{3\log(\sqrt{2}+1)d}{8}+\frac{d}{8\left(\sqrt{2}+1\right)^{2\log(e)}}-\frac{d}{64\left(\sqrt{2}+1\right)^{4\log(e)}}$$

Differensier med hensyn til d

$$\frac{1}{8\left(\sqrt{2}+1\right)^{2\log(e)}}+\frac{3\log(\sqrt{2}+1)}{8}+\frac{\left(\sqrt{2}+1\right)^{4\log(e)}}{64}-\frac{1}{64\left(\sqrt{2}+1\right)^{4\log(e)}}-\frac{\left(\sqrt{2}+1\right)^{2\log(e)}}{8}$$