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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
Solving integrals/ x^2*sin^7(x)

Integral of x^2*sin^7(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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-pi
∫−ππx2sin⁡7(x) dx\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] 
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 |                               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          
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∫x2sin⁡7(x) dx=C−x2sin⁡6(x)cos⁡(x)−2x2sin⁡4(x)cos⁡3(x)−8x2sin⁡2(x)cos⁡5(x)5−16x2cos⁡7(x)35+4322xsin⁡7(x)3675+1636xsin⁡5(x)cos⁡2(x)525+304xsin⁡3(x)cos⁡4(x)105+32xsin⁡(x)cos⁡6(x)35+4322sin⁡6(x)cos⁡(x)3675+37384sin⁡4(x)cos⁡3(x)11025+181456sin⁡2(x)cos⁡5(x)55125+413312cos⁡7(x)385875\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}
Simplify
The graph
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.05-5
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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