Sr Examen
Integral de sin^2(2x+5) dx
Solución
Ha introducido
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1 / | | 2 | sin (2*x + 5) dx | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(2 x + 5 \right)}\, dx$$
Integral(sin(2*x + 5)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 4 2 | 2 x tan (5/2 + x) tan(5/2 + x) x*tan (5/2 + x) 2*x*tan (5/2 + x) | sin (2*x + 5) dx = C + ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ------------------------------------- | 4 2 4 2 4 2 4 2 4 2 / 2 + 2*tan (5/2 + x) + 4*tan (5/2 + x) 2 + 2*tan (5/2 + x) + 4*tan (5/2 + x) 2 + 2*tan (5/2 + x) + 4*tan (5/2 + x) 2 + 2*tan (5/2 + x) + 4*tan (5/2 + x) 2 + 2*tan (5/2 + x) + 4*tan (5/2 + x)
$$\int \sin^{2}{\left(2 x + 5 \right)}\, dx = C + \frac{x \tan^{4}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} + \frac{\tan^{3}{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2} - \frac{\tan{\left(x + \frac{5}{2} \right)}}{2 \tan^{4}{\left(x + \frac{5}{2} \right)} + 4 \tan^{2}{\left(x + \frac{5}{2} \right)} + 2}$$
Gráfica
Respuesta
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2 2 cos (7) sin (7) cos(7)*sin(7) cos(5)*sin(5) ------- + ------- - ------------- + ------------- 2 2 4 4
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{4} + \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{4} + \frac{\sin^{2}{\left(7 \right)}}{2} + \frac{\cos^{2}{\left(7 \right)}}{2}$$
=
=
2 2 cos (7) sin (7) cos(7)*sin(7) cos(5)*sin(5) ------- + ------- - ------------- + ------------- 2 2 4 4
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{4} + \frac{\sin{\left(5 \right)} \cos{\left(5 \right)}}{4} + \frac{\sin^{2}{\left(7 \right)}}{2} + \frac{\cos^{2}{\left(7 \right)}}{2}$$
cos(7)^2/2 + sin(7)^2/2 - cos(7)*sin(7)/4 + cos(5)*sin(5)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.