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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^2dx
- Integral of x/y
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Integral of exp(2x)
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Integral of dx/(1+e^x)
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Identical expressions
- (sin^ four)(x)*cosx
- ( sinus of to the power of 4)(x) multiply by co sinus of e of x
- ( sinus of to the power of four)(x) multiply by co sinus of e of x
- (sin4)(x)*cosx
- sin4x*cosx
- (sin⁴)(x)*cosx
- (sin^4)(x)cosx
- (sin4)(x)cosx
- sin4xcosx
- sin^4xcosx
- (sin^4)(x)*cosxdx
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Similar expressions
- sin^4x*cos(x)
Integral of (sin^4)(x)*cosx dx
The solution
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pi -- 4 / | | 4 | sin (x)*x*cos(x) dx | / pi -- 6
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((sin(x)^4*x)*cos(x), (x, pi/6, pi/4))
The answer (Indefinite)
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/ | 5 5 4 3 2 | 4 8*cos (x) x*sin (x) sin (x)*cos(x) 4*cos (x)*sin (x) | sin (x)*x*cos(x) dx = C + --------- + --------- + -------------- + ----------------- | 75 5 5 15 /
$$\int x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{x \sin^{5}{\left(x \right)}}{5} + \frac{\sin^{4}{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{15} + \frac{8 \cos^{5}{\left(x \right)}}{75}$$
The graph
The answer
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___ ___ ___
49*\/ 3 pi 43*\/ 2 pi*\/ 2
- -------- - --- + -------- + --------
800 960 600 160
$$- \frac{49 \sqrt{3}}{800} - \frac{\pi}{960} + \frac{\sqrt{2} \pi}{160} + \frac{43 \sqrt{2}}{600}$$
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___ ___ ___
49*\/ 3 pi 43*\/ 2 pi*\/ 2
- -------- - --- + -------- + --------
800 960 600 160
$$- \frac{49 \sqrt{3}}{800} - \frac{\pi}{960} + \frac{\sqrt{2} \pi}{160} + \frac{43 \sqrt{2}}{600}$$
-49*sqrt(3)/800 - pi/960 + 43*sqrt(2)/600 + pi*sqrt(2)/160
Use the examples entering the upper and lower limits of integration.