Exercício
$\int x^6\sqrt{x^2+1}dx$
Solução explicada passo a passo
Resposta final para o problema
$\frac{35}{128}\ln\left|\sqrt{x^2+1}+x\right|+\frac{35}{128}\sqrt{x^2+1}x+\frac{35}{192}\sqrt{\left(x^2+1\right)^{3}}x+\frac{7}{48}\sqrt{\left(x^2+1\right)^{5}}x+\frac{x\sqrt{\left(x^2+1\right)^{7}}}{8}-\frac{15}{16}\ln\left|\sqrt{x^2+1}+x\right|-\frac{15}{16}\sqrt{x^2+1}x-\frac{5}{8}\sqrt{\left(x^2+1\right)^{3}}x-\frac{1}{2}\sqrt{\left(x^2+1\right)^{5}}x+\frac{9}{8}\ln\left|\sqrt{x^2+1}+x\right|+\frac{9}{8}\sqrt{x^2+1}x+\frac{3}{4}\sqrt{\left(x^2+1\right)^{3}}x-\frac{1}{2}\ln\left|\sqrt{x^2+1}+x\right|+\frac{-x\sqrt{x^2+1}}{2}+C_0$