Sr Examen
Integral de 5^(-x)*cos(nx) dx
Solución
Ha introducido
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1 / | | -x | 5 *cos(n*x) dx | / 0
$$\int\limits_{0}^{1} 5^{- x} \cos{\left(n x \right)}\, dx$$
Integral(5^(-x)*cos(n*x), (x, 0, 1))
Respuesta (Indefinida)
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/ | | -x n*sin(n*x) cos(n*x)*log(5) | 5 *cos(n*x) dx = C + ------------------ - ------------------ | x 2 x 2 x 2 x 2 / 5 *n + 5 *log (5) 5 *n + 5 *log (5)
$$\int 5^{- x} \cos{\left(n x \right)}\, dx = C + \frac{n \sin{\left(n x \right)}}{5^{x} n^{2} + 5^{x} \log{\left(5 \right)}^{2}} - \frac{\log{\left(5 \right)} \cos{\left(n x \right)}}{5^{x} n^{2} + 5^{x} \log{\left(5 \right)}^{2}}$$
Respuesta
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log(5) n*sin(n) cos(n)*log(5) ------------ + ---------------- - ---------------- 2 2 2 2 2 2 n + log (5) 5*n + 5*log (5) 5*n + 5*log (5)
$$\frac{n \sin{\left(n \right)}}{5 n^{2} + 5 \log{\left(5 \right)}^{2}} - \frac{\log{\left(5 \right)} \cos{\left(n \right)}}{5 n^{2} + 5 \log{\left(5 \right)}^{2}} + \frac{\log{\left(5 \right)}}{n^{2} + \log{\left(5 \right)}^{2}}$$
=
=
log(5) n*sin(n) cos(n)*log(5) ------------ + ---------------- - ---------------- 2 2 2 2 2 2 n + log (5) 5*n + 5*log (5) 5*n + 5*log (5)
$$\frac{n \sin{\left(n \right)}}{5 n^{2} + 5 \log{\left(5 \right)}^{2}} - \frac{\log{\left(5 \right)} \cos{\left(n \right)}}{5 n^{2} + 5 \log{\left(5 \right)}^{2}} + \frac{\log{\left(5 \right)}}{n^{2} + \log{\left(5 \right)}^{2}}$$
log(5)/(n^2 + log(5)^2) + n*sin(n)/(5*n^2 + 5*log(5)^2) - cos(n)*log(5)/(5*n^2 + 5*log(5)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.