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