Sr Examen
Integral de 1/(2*x+sqrt(3*x+1)) dx
Solución
Ha introducido
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5 / | | 1 | ----------------- dx | _________ | 2*x + \/ 3*x + 1 | / 0
$$\int\limits_{0}^{5} \frac{1}{2 x + \sqrt{3 x + 1}}\, dx$$
Integral(1/(2*x + sqrt(3*x + 1)), (x, 0, 5))
Respuesta (Indefinida)
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/ | / _________ \ / _________\ / _________\ | 1 log\3*\/ 3*x + 1 + 6*x/ 3*log\-2 + 4*\/ 3*x + 1 / 3*log\8 + 4*\/ 3*x + 1 / | ----------------- dx = C + ------------------------ - ------------------------- + ------------------------ | _________ 2 10 10 | 2*x + \/ 3*x + 1 | /
$$\int \frac{1}{2 x + \sqrt{3 x + 1}}\, dx = C + \frac{\log{\left(6 x + 3 \sqrt{3 x + 1} \right)}}{2} - \frac{3 \log{\left(4 \sqrt{3 x + 1} - 2 \right)}}{10} + \frac{3 \log{\left(4 \sqrt{3 x + 1} + 8 \right)}}{10}$$
Gráfica
Respuesta
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log(42) 3*log(12) 3*log(14) log(3) 3*log(2) 3*log(24) ------- - --------- - --------- - ------ + -------- + --------- 2 10 10 2 10 10
$$- \frac{3 \log{\left(14 \right)}}{10} - \frac{3 \log{\left(12 \right)}}{10} - \frac{\log{\left(3 \right)}}{2} + \frac{3 \log{\left(2 \right)}}{10} + \frac{3 \log{\left(24 \right)}}{10} + \frac{\log{\left(42 \right)}}{2}$$
=
=
log(42) 3*log(12) 3*log(14) log(3) 3*log(2) 3*log(24) ------- - --------- - --------- - ------ + -------- + --------- 2 10 10 2 10 10
$$- \frac{3 \log{\left(14 \right)}}{10} - \frac{3 \log{\left(12 \right)}}{10} - \frac{\log{\left(3 \right)}}{2} + \frac{3 \log{\left(2 \right)}}{10} + \frac{3 \log{\left(24 \right)}}{10} + \frac{\log{\left(42 \right)}}{2}$$
log(42)/2 - 3*log(12)/10 - 3*log(14)/10 - log(3)/2 + 3*log(2)/10 + 3*log(24)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.