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How to use it?
- Integral of d{x}:
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Integral of sin^4xcos^4xdx
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Integral of xarcctgxdx
- Integral of x^2*sin^7(x)
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Integral of 〖ctg^2xdx〗
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Identical expressions
- x^ two *sin^ seven (x)
- x squared multiply by sinus of to the power of 7(x)
- x to the power of two multiply by sinus of to the power of seven (x)
- x2*sin7(x)
- x2*sin7x
- x²*sin⁷(x)
- x to the power of 2*sin to the power of 7(x)
- x^2sin^7(x)
- x2sin7(x)
- x2sin7x
- x^2sin^7x
- x^2*sin^7(x)dx
Integral of x^2*sin^7(x) dx
The solution
You have entered
[src]
pi / | | 2 7 | x *sin (x) dx | / -pi
$$\int\limits_{- \pi}^{\pi} x^{2} \sin^{7}{\left(x \right)}\, dx$$
Integral(x^2*sin(x)^7, (x, -pi, pi))
The answer (Indefinite)
[src]
/ | 7 2 7 7 6 3 4 5 2 2 5 2 6 4 3 2 5 | 2 7 413312*cos (x) 16*x *cos (x) 4322*x*sin (x) 4322*sin (x)*cos(x) 37384*cos (x)*sin (x) 181456*cos (x)*sin (x) 2 6 2 3 4 8*x *cos (x)*sin (x) 32*x*cos (x)*sin(x) 304*x*cos (x)*sin (x) 1636*x*cos (x)*sin (x) | x *sin (x) dx = C + -------------- - ------------- + -------------- + ------------------- + --------------------- + ---------------------- - x *sin (x)*cos(x) - 2*x *cos (x)*sin (x) - -------------------- + ------------------- + --------------------- + ---------------------- | 385875 35 3675 3675 11025 55125 5 35 105 525 /
$$\int x^{2} \sin^{7}{\left(x \right)}\, dx = C - x^{2} \sin^{6}{\left(x \right)} \cos{\left(x \right)} - 2 x^{2} \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)} - \frac{8 x^{2} \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{5} - \frac{16 x^{2} \cos^{7}{\left(x \right)}}{35} + \frac{4322 x \sin^{7}{\left(x \right)}}{3675} + \frac{1636 x \sin^{5}{\left(x \right)} \cos^{2}{\left(x \right)}}{525} + \frac{304 x \sin^{3}{\left(x \right)} \cos^{4}{\left(x \right)}}{105} + \frac{32 x \sin{\left(x \right)} \cos^{6}{\left(x \right)}}{35} + \frac{4322 \sin^{6}{\left(x \right)} \cos{\left(x \right)}}{3675} + \frac{37384 \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)}}{11025} + \frac{181456 \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{55125} + \frac{413312 \cos^{7}{\left(x \right)}}{385875}$$
The graph
Use the examples entering the upper and lower limits of integration.