Übung
$\int_{-3x^2}^{6x^3}\left(t^4\right)\left(\sqrt{t^2+1}\right)dt$
Schritt-für-Schritt-Lösung
Endgültige Antwort auf das Problem
$-\frac{5}{16}\ln\left|\sqrt{\left(-3x^2\right)^2+1}-3x^2\right|+\frac{15}{16}\sqrt{\left(-3x^2\right)^2+1}x^2+\frac{5}{8}\sqrt{\left(\left(-3x^2\right)^2+1\right)^{3}}x^2+\frac{1}{2}\sqrt{\left(\left(-3x^2\right)^2+1\right)^{5}}x^2+\frac{5}{16}\ln\left|\sqrt{\left(6x^3\right)^2+1}+6x^3\right|+\frac{39}{8}x^3\sqrt{36x^{6}+1}-\frac{7}{4}\sqrt{\left(36x^{6}+1\right)^{3}}x^3+\sqrt{\left(36x^{6}+1\right)^{5}}x^3+\frac{3}{4}\ln\left|\sqrt{\left(-3x^2\right)^2+1}-3x^2\right|-\frac{9}{4}\sqrt{\left(-3x^2\right)^2+1}x^2-\frac{3}{2}\sqrt{\left(\left(-3x^2\right)^2+1\right)^{3}}x^2-\frac{3}{4}\ln\left|\sqrt{36x^{6}+1}+6x^3\right|-\frac{9}{2}\sqrt{36x^{6}+1}x^3-\left(\frac{-3x^2\sqrt{\left(-3x^2\right)^2+1}}{2}+\frac{1}{2}\ln\left|\sqrt{\left(-3x^2\right)^2+1}-3x^2\right|\right)+\frac{1}{2}\ln\left|\sqrt{\left(6x^3\right)^2+1}+6x^3\right|$