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Identical expressions
- x^ three *cos^ three (x)
- x cubed multiply by co sinus of e of cubed (x)
- x to the power of three multiply by co sinus of e of to the power of three (x)
- x3*cos3(x)
- x3*cos3x
- x³*cos³(x)
- x to the power of 3*cos to the power of 3(x)
- x^3cos^3(x)
- x3cos3(x)
- x3cos3x
- x^3cos^3x
- x^3*cos^3(x)dx
Integral of x^3*cos^3(x) dx
The solution
You have entered
[src]
1 / | | 3 3 | x *cos (x) dx | / -1
$$\int\limits_{-1}^{1} x^{3} \cos^{3}{\left(x \right)}\, dx$$
Integral(x^3*cos(x)^3, (x, -1, 1))
The answer (Indefinite)
[src]
/ | 3 3 2 3 3 2 3 2 | 3 3 122*cos (x) 40*x*sin (x) 40*sin (x)*cos(x) 2*x *sin (x) 7*x *cos (x) 3 2 2 2 14*x*cos (x)*sin(x) | x *cos (x) dx = C - ----------- - ------------ - ----------------- + ------------ + ------------ + x *cos (x)*sin(x) + 2*x *sin (x)*cos(x) - ------------------- | 27 9 9 3 3 3 /
$$\int x^{3} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{3} \sin^{3}{\left(x \right)}}{3} + x^{3} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 2 x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{7 x^{2} \cos^{3}{\left(x \right)}}{3} - \frac{40 x \sin^{3}{\left(x \right)}}{9} - \frac{14 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - \frac{40 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} - \frac{122 \cos^{3}{\left(x \right)}}{27}$$
The graph
Use the examples entering the upper and lower limits of integration.