Question

2∫4xdx/2(x²+3)^4
Integral

Answer 1

Resposta:

-\frac{2}{3(x^{2}+3)^{3}}+c[/tex]

Explicação passo-a-passo:

x² + 3 = u ⇒ 2xdx = du ⇒ xdx = 1/2 du

$2\int\limits_ {}\frac{4xdx}{2(x^{2}+3)^{4}}\, dx=\frac{2.4}{2}\int\limits_ {}\frac{xdx}{(x^{2}+3)^{4} }^{}\,=4\int\limits_ {}\frac{\frac{1}{2}du }{u^{4}}\,= 4.\frac{1}{2}\int\limits_ {}\,u^{-4}du=2\int\limits_ {}u^{-4}du\,=2.\frac{u^{-4+1}}{-4+1}+c=\frac{2}{-3}*u^{-3}+ c=-\frac{2}{3}*\frac{1}{u^{3}}+c=-\frac{2}{3(x^{2}+3)^{3}}+c$