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- Improper integral
- Double Integral
- Triple Integral
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How to use it?
- Integral of d{x}:
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Integral of (x^2+1)/((x^3+3x+1)^5)
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Integral of sqrt(x^2+1)*dx/x
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Integral of sqrt(1-x^2)/x^2
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Integral of (x-1)^1/2
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Identical expressions
- (cos^ four)x*sinx
- ( co sinus of e of to the power of 4)x multiply by sinus of x
- ( co sinus of e of to the power of four)x multiply by sinus of x
- (cos4)x*sinx
- cos4x*sinx
- (cos⁴)x*sinx
- (cos^4)xsinx
- (cos4)xsinx
- cos4xsinx
- cos^4xsinx
- (cos^4)x*sinxdx
Integral of (cos^4)x*sinx dx
The solution
You have entered
[src]
pi -- 2 / | | 4 | cos (x)*x*sin(x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} x \cos^{4}{\left(x \right)} \sin{\left(x \right)}\, dx$$
Integral((cos(x)^4*x)*sin(x), (x, 0, pi/2))
The answer (Indefinite)
[src]
/ | 5 5 4 2 3 | 4 8*sin (x) x*cos (x) cos (x)*sin(x) 4*cos (x)*sin (x) | cos (x)*x*sin(x) dx = C + --------- - --------- + -------------- + ----------------- | 75 5 5 15 /
$$\int x \cos^{4}{\left(x \right)} \sin{\left(x \right)}\, dx = C - \frac{x \cos^{5}{\left(x \right)}}{5} + \frac{8 \sin^{5}{\left(x \right)}}{75} + \frac{4 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{15} + \frac{\sin{\left(x \right)} \cos^{4}{\left(x \right)}}{5}$$
The graph
Use the examples entering the upper and lower limits of integration.