Найти интеграл ∫x³*√x^4+1 dx

[latex]\int x^3 \sqrt{x^4+1} dx=\frac{1}{4} \int 4x^3 (x^4+1)^{\frac{1}{2}}dx=[/latex] [latex]\frac{1}{4} \int (x^4+1)^{\frac{1}{2}} d(x^4)=[/latex] [latex]\frac{1}{4} \int (x^4+1)^{\frac{1}{2}} d(x^4+1)=[/latex] [latex]\frac{1}{4} *\frac{(x^4+1)^{\frac{1}{2}+1}}{\frac{1}{2}+1}[/latex] [latex]\frac{1}{4}*\frac{2}{3}*(x^4+1)^{\frac{3}{2}}=[/latex] [latex]\frac{(x^4+1)\sqrt{x^4+1}}{6}[/latex]