Question

integral x raiz de x+1 dx​

Answer 1

Resposta:

Explicação passo-a-passo:

$\int\limits {x*\sqrt{x+1} \, dx =$

chamamos x+1=u

logo du= dx

Temos também, se x+1= u => x= u-1

$\int\limits {(u-1)*u^{\frac{1}{2}} \, dx =  \ fazendo \ a \ distributiva \\\\\\\\\int{(u^{\frac{3}{2}}-u^{\frac{1}{2}}) dx=\\\\\\\int{u^{\frac{3}{2}}dx -\int{u^{\frac{1}{2}}dx =\\\\\frac{u^{\frac{5}{2}}}{\frac{5}{2}} -\frac{u^{\frac{3}{2}}}{\frac{3}{2}} +C =\\\\\frac{2*u^{\frac{5}{2}}}{5}- \frac{2*u^{\frac{3}{2}}}{3}}+C=\\\\\frac{2}{5}*(x+1)^{\frac{5}{2}}-\frac{2}{3}*(x+1)^{\frac{3}{2}}+C$