• Matéria: Matemática
  • Autor: thoomaz2
  • Perguntado 8 anos atrás

alguém sabe responder integral e substituição em u

Anexos:

francof23: o e ta elevado a 2x ou soh a 2 msm?
thoomaz2: a 2x

Respostas

respondido por: francof23
0
\int{\dfrac{e^{2x}}{4+e^{2x}}} \ dx\\\\\\u=4+e^{2x}\\\\\\du=2e^{2x}\ dx\\\\\\dx=\dfrac{du}{2e^{2x}}\\\\\\\int{\dfrac{e^{2x}}{4+e^{2x}}} \ \dfrac{du}{2e^{2x}}\\\\\\\int{\dfrac{1}{2u}} \ du\\\\\\\dfrac12\ln|u|+C\\\\\\\dfrac{1}{2}\ln(4+e^{2x})+C
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