Sr Examen
Integral de cos^7xsindx dx
Solución
Ha introducido
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1 / | | 7 | cos (x)*sin(d)*x dx | / 0
$$\int\limits_{0}^{1} x \sin{\left(d \right)} \cos^{7}{\left(x \right)}\, dx$$
Integral((cos(x)^7*sin(d))*x, (x, 0, 1))
Respuesta (Indefinida)
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/ | / 7 7 6 3 4 5 2 2 5 \ | 7 |2161*cos (x) 16*x*sin (x) 16*sin (x)*cos(x) 152*cos (x)*sin (x) 818*cos (x)*sin (x) 6 4 3 8*x*cos (x)*sin (x)| | cos (x)*sin(d)*x dx = C + |------------ + ------------ + ----------------- + ------------------- + ------------------- + x*cos (x)*sin(x) + 2*x*cos (x)*sin (x) + -------------------|*sin(d) | \ 3675 35 35 105 525 5 / /
$$\int x \sin{\left(d \right)} \cos^{7}{\left(x \right)}\, dx = C + \left(\frac{16 x \sin^{7}{\left(x \right)}}{35} + \frac{8 x \sin^{5}{\left(x \right)} \cos^{2}{\left(x \right)}}{5} + 2 x \sin^{3}{\left(x \right)} \cos^{4}{\left(x \right)} + x \sin{\left(x \right)} \cos^{6}{\left(x \right)} + \frac{16 \sin^{6}{\left(x \right)} \cos{\left(x \right)}}{35} + \frac{152 \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)}}{105} + \frac{818 \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{525} + \frac{2161 \cos^{7}{\left(x \right)}}{3675}\right) \sin{\left(d \right)}$$
Respuesta
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/ 7 7 2 5 6 3 4 5 2 \
2161*sin(d) |16*sin (1) 2161*cos (1) 6 4 3 8*cos (1)*sin (1) 16*sin (1)*cos(1) 152*cos (1)*sin (1) 818*cos (1)*sin (1)|
- ----------- + |---------- + ------------ + cos (1)*sin(1) + 2*cos (1)*sin (1) + ----------------- + ----------------- + ------------------- + -------------------|*sin(d)
3675 \ 35 3675 5 35 105 525 /
$$- \frac{2161 \sin{\left(d \right)}}{3675} + \left(\frac{2161 \cos^{7}{\left(1 \right)}}{3675} + \sin{\left(1 \right)} \cos^{6}{\left(1 \right)} + \frac{818 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{525} + \frac{16 \sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{35} + 2 \sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)} + \frac{152 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{105} + \frac{16 \sin^{7}{\left(1 \right)}}{35} + \frac{8 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{5}\right) \sin{\left(d \right)}$$
=
=
/ 7 7 2 5 6 3 4 5 2 \
2161*sin(d) |16*sin (1) 2161*cos (1) 6 4 3 8*cos (1)*sin (1) 16*sin (1)*cos(1) 152*cos (1)*sin (1) 818*cos (1)*sin (1)|
- ----------- + |---------- + ------------ + cos (1)*sin(1) + 2*cos (1)*sin (1) + ----------------- + ----------------- + ------------------- + -------------------|*sin(d)
3675 \ 35 3675 5 35 105 525 /
$$- \frac{2161 \sin{\left(d \right)}}{3675} + \left(\frac{2161 \cos^{7}{\left(1 \right)}}{3675} + \sin{\left(1 \right)} \cos^{6}{\left(1 \right)} + \frac{818 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{525} + \frac{16 \sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{35} + 2 \sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)} + \frac{152 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{105} + \frac{16 \sin^{7}{\left(1 \right)}}{35} + \frac{8 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{5}\right) \sin{\left(d \right)}$$
-2161*sin(d)/3675 + (16*sin(1)^7/35 + 2161*cos(1)^7/3675 + cos(1)^6*sin(1) + 2*cos(1)^4*sin(1)^3 + 8*cos(1)^2*sin(1)^5/5 + 16*sin(1)^6*cos(1)/35 + 152*cos(1)^3*sin(1)^4/105 + 818*cos(1)^5*sin(1)^2/525)*sin(d)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.