Question

calcule a integral definida raiz cubica de 7+x⁵x⁴ dx​

Answer 1

Resposta:

Explicação passo-a-passo:

$\int\sqrt[3]{7+x^{5} }{x^{4}}\,dx$

faça

$u=7+x^{5}\\du=5x^{4}dx$

Multiplique e divida a integral por 5

$\dfrac{1}{5}\int\sqrt[3]{7+x^{5}}{5x^{4}}\,dx=\\\\=\dfrac{1}{5}\int\sqrt[3]{u}}\,du=\dfrac{1}{5}\int\ u^{\frac{1}{3}}}\,du=\dfrac{1}{5}\dfrac{u^{\frac{1}{3}+1}}{\frac{1}{3}+1}+C=\\\\=\dfrac{1}{5}\dfrac{u^{\frac{4}{3}}}{\frac{4}{3}}+C=\dfrac{1}{5}.\dfrac{3}{4}.u^{\frac{4}{3}}+C=\\\\\\=\dfrac{3}{20}.(7+x^{5})^{\frac{4}{3}}+C$