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How to use it?
- Integral of d{x}:
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Integral of xln(x)
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Integral of x*2
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Integral of x*dx/(x+1)
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Integral of e^2x
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Identical expressions
- (x- three y)dx/ two (x-y)^(3/ two)
- (x minus 3y)dx divide by 2(x minus y) to the power of (3 divide by 2)
- (x minus three y)dx divide by two (x minus y) to the power of (3 divide by two)
- (x-3y)dx/2(x-y)(3/2)
- x-3ydx/2x-y3/2
- x-3ydx/2x-y^3/2
- (x-3y)dx divide by 2(x-y)^(3 divide by 2)
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Similar expressions
- (x+3y)dx/2(x-y)^(3/2)
- (x-3y)dx/2(x+y)^(3/2)
Integral of (x-3y)dx/2(x-y)^(3/2) dx
The solution
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[src]
1 / | | x - 3*y 3/2 | -------*(x - y) dx | 2 | / 0
$$\int\limits_{0}^{1} \frac{x - 3 y}{2} \left(x - y\right)^{\frac{3}{2}}\, dx$$
Integral(((x - 3*y)/2)*(x - y)^(3/2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 7/2 / 5/2 3/2\ 5/2 2 3/2 | x - 3*y 3/2 (x - y) |2*(x - y) 2*y*(x - y) | 2*y*(x - y) 4*y *(x - y) | -------*(x - y) dx = C + ---------- - 2*y*|------------ + --------------| + -------------- + --------------- | 2 7 \ 5 3 / 5 3 | /
$$\int \frac{x - 3 y}{2} \left(x - y\right)^{\frac{3}{2}}\, dx = C + \frac{4 y^{2} \left(x - y\right)^{\frac{3}{2}}}{3} + \frac{2 y \left(x - y\right)^{\frac{5}{2}}}{5} - 2 y \left(\frac{2 y \left(x - y\right)^{\frac{3}{2}}}{3} + \frac{2 \left(x - y\right)^{\frac{5}{2}}}{5}\right) + \frac{\left(x - y\right)^{\frac{7}{2}}}{7}$$
The answer
[src]
_______ _______ 3 _______ 3 ____ 2 _______
\/ 1 - y 29*y*\/ 1 - y 19*y *\/ 1 - y 19*y *\/ -y 43*y *\/ 1 - y
--------- - -------------- - --------------- + ------------ + ---------------
7 35 35 35 35
$$\frac{19 y^{3} \sqrt{- y}}{35} - \frac{19 y^{3} \sqrt{1 - y}}{35} + \frac{43 y^{2} \sqrt{1 - y}}{35} - \frac{29 y \sqrt{1 - y}}{35} + \frac{\sqrt{1 - y}}{7}$$
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_______ _______ 3 _______ 3 ____ 2 _______
\/ 1 - y 29*y*\/ 1 - y 19*y *\/ 1 - y 19*y *\/ -y 43*y *\/ 1 - y
--------- - -------------- - --------------- + ------------ + ---------------
7 35 35 35 35
$$\frac{19 y^{3} \sqrt{- y}}{35} - \frac{19 y^{3} \sqrt{1 - y}}{35} + \frac{43 y^{2} \sqrt{1 - y}}{35} - \frac{29 y \sqrt{1 - y}}{35} + \frac{\sqrt{1 - y}}{7}$$
sqrt(1 - y)/7 - 29*y*sqrt(1 - y)/35 - 19*y^3*sqrt(1 - y)/35 + 19*y^3*sqrt(-y)/35 + 43*y^2*sqrt(1 - y)/35
Use the examples entering the upper and lower limits of integration.