Sr Examen
Integral de (3-2x^4+3^sqrt(x6^2))/(4^sqrt(x)) dx
Solución
Ha introducido
[src]
1 / | | _____ | / 2 | 4 \/ x6 | 3 - 2*x + 3 | -------------------- dx | ___ | \/ x | 4 | / 0
$$\int\limits_{0}^{1} \frac{3^{\sqrt{x_{6}^{2}}} + \left(3 - 2 x^{4}\right)}{4^{\sqrt{x}}}\, dx$$
Integral((3 - 2*x^4 + 3^(sqrt(x6^2)))/4^(sqrt(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ | | _____ | / 2 _____ / ___ ___ \ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ | 4 \/ x6 / 2 | -\/ x -\/ x ___| -\/ x -\/ x -\/ x ___ -\/ x 9/2 -\/ x 4 -\/ x 7/2 -\/ x 3 -\/ x 5/2 -\/ x 2 -\/ x 3/2 -\/ x -\/ x ___ | 3 - 2*x + 3 \/ x6 | 4 4 *\/ x | 3*4 2835*4 3*4 *\/ x 2*4 *x 9*4 *x 36*4 *x 126*4 *x 378*4 *x 945*4 *x 1890*4 *x 2835*x*4 2835*4 *\/ x | -------------------- dx = C + 3 *|- --------- - -------------| - --------- + ------------ - --------------- + -------------- + ------------ + --------------- + -------------- + ---------------- + -------------- + ----------------- + -------------- + ------------------ | ___ | 2 log(2) | 2 10 log(2) log(2) 2 3 4 5 6 7 8 9 | \/ x \ 2*log (2) / 2*log (2) 2*log (2) log (2) log (2) log (2) log (2) log (2) log (2) log (2) log (2) | 4 | /
$$\int \frac{3^{\sqrt{x_{6}^{2}}} + \left(3 - 2 x^{4}\right)}{4^{\sqrt{x}}}\, dx = 3^{\sqrt{x_{6}^{2}}} \left(- \frac{4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}} - \frac{4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{2}}\right) + C + \frac{2 \cdot 4^{- \sqrt{x}} x^{\frac{9}{2}}}{\log{\left(2 \right)}} + \frac{36 \cdot 4^{- \sqrt{x}} x^{\frac{7}{2}}}{\log{\left(2 \right)}^{3}} + \frac{378 \cdot 4^{- \sqrt{x}} x^{\frac{5}{2}}}{\log{\left(2 \right)}^{5}} + \frac{1890 \cdot 4^{- \sqrt{x}} x^{\frac{3}{2}}}{\log{\left(2 \right)}^{7}} - \frac{3 \cdot 4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}} + \frac{2835 \cdot 4^{- \sqrt{x}} \sqrt{x}}{\log{\left(2 \right)}^{9}} + \frac{9 \cdot 4^{- \sqrt{x}} x^{4}}{\log{\left(2 \right)}^{2}} + \frac{126 \cdot 4^{- \sqrt{x}} x^{3}}{\log{\left(2 \right)}^{4}} + \frac{945 \cdot 4^{- \sqrt{x}} x^{2}}{\log{\left(2 \right)}^{6}} + \frac{2835 \cdot 4^{- \sqrt{x}} x}{\log{\left(2 \right)}^{8}} - \frac{3 \cdot 4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{2}} + \frac{2835 \cdot 4^{- \sqrt{x}}}{2 \log{\left(2 \right)}^{10}}$$
Respuesta
[src]
_____ _____
/ 2 / 2
\/ x6 \/ x6
9 8505 1 27 63 189 945 945 2835 2835 3 3*3
------- - ---------- - -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- - --------- + -----------
3 10 4*log(2) 2 4 5 7 6 9 8 4*log(2) 2
log (2) 8*log (2) 8*log (2) 2*log (2) 2*log (2) 2*log (2) 4*log (2) 4*log (2) 4*log (2) 8*log (2)
$$- \frac{3^{\sqrt{x_{6}^{2}}}}{4 \log{\left(2 \right)}} + \frac{3 \cdot 3^{\sqrt{x_{6}^{2}}}}{8 \log{\left(2 \right)}^{2}} - \frac{8505}{8 \log{\left(2 \right)}^{10}} - \frac{1}{4 \log{\left(2 \right)}} + \frac{27}{8 \log{\left(2 \right)}^{2}} + \frac{9}{\log{\left(2 \right)}^{3}} + \frac{63}{2 \log{\left(2 \right)}^{4}} + \frac{189}{2 \log{\left(2 \right)}^{5}} + \frac{945}{4 \log{\left(2 \right)}^{6}} + \frac{945}{2 \log{\left(2 \right)}^{7}} + \frac{2835}{4 \log{\left(2 \right)}^{8}} + \frac{2835}{4 \log{\left(2 \right)}^{9}}$$
=
=
_____ _____
/ 2 / 2
\/ x6 \/ x6
9 8505 1 27 63 189 945 945 2835 2835 3 3*3
------- - ---------- - -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- - --------- + -----------
3 10 4*log(2) 2 4 5 7 6 9 8 4*log(2) 2
log (2) 8*log (2) 8*log (2) 2*log (2) 2*log (2) 2*log (2) 4*log (2) 4*log (2) 4*log (2) 8*log (2)
$$- \frac{3^{\sqrt{x_{6}^{2}}}}{4 \log{\left(2 \right)}} + \frac{3 \cdot 3^{\sqrt{x_{6}^{2}}}}{8 \log{\left(2 \right)}^{2}} - \frac{8505}{8 \log{\left(2 \right)}^{10}} - \frac{1}{4 \log{\left(2 \right)}} + \frac{27}{8 \log{\left(2 \right)}^{2}} + \frac{9}{\log{\left(2 \right)}^{3}} + \frac{63}{2 \log{\left(2 \right)}^{4}} + \frac{189}{2 \log{\left(2 \right)}^{5}} + \frac{945}{4 \log{\left(2 \right)}^{6}} + \frac{945}{2 \log{\left(2 \right)}^{7}} + \frac{2835}{4 \log{\left(2 \right)}^{8}} + \frac{2835}{4 \log{\left(2 \right)}^{9}}$$
9/log(2)^3 - 8505/(8*log(2)^10) - 1/(4*log(2)) + 27/(8*log(2)^2) + 63/(2*log(2)^4) + 189/(2*log(2)^5) + 945/(2*log(2)^7) + 945/(4*log(2)^6) + 2835/(4*log(2)^9) + 2835/(4*log(2)^8) - 3^(sqrt(x6^2))/(4*log(2)) + 3*3^(sqrt(x6^2))/(8*log(2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.