• Matéria: Matemática
  • Autor: fernandodesouza
  • Perguntado 9 anos atrás

resolva a integral ∫ 4x^3 sen(3x^4-5) dx

Respostas

respondido por: Niiya
5
\int4x^{3}sen(3x^{4}-5)dx

Seja u = 3x⁴ - 5:

u=3x^{4}-5~~~~~~~~~(derivando:)\\du=3\cdot4x^{3}dx~~~~~~(isolando~4x^{3}dx:)\\\\\\\boxed{\boxed{4x^{3}dx=\dfrac{1}{3}du}}

Então:

\int4x^{3}sen(3x^{4}-5)dx=\int sen(3x^{4}-5)\cdot4x^{3}dx\\\\\int4x^{3}sen(3x^{4}-5)dx=\int sen(u)\cdot\frac{1}{3}du\\\\\int4x^{3}sen(3x^{4}-5)dx=\frac{1}{3}\int sen(u)du\\\\\int4x^{3}sen(3x^{4}-5)dx=\frac{1}{3}(-cos~(u))+C

Voltando para a variável x:

\boxed{\boxed{\int4x^{3}sen(3x^{4}-5)dx=-\dfrac{cos(3x^{4}-5)}{3}+C}}
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