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Identical expressions
u=xsiny+e^x-3y^ two
u equally x sinus of y plus e to the power of x minus 3y squared
u equally x sinus of y plus e to the power of x minus 3y to the power of two
u=xsiny+ex-3y2
u=xsiny+e^x-3y²
u=xsiny+e to the power of x-3y to the power of 2
u=xsiny+e^x-3y^2dx
Similar expressions
u=xsiny+e^x+3y^2
u=xsiny-e^x-3y^2

Integral of u=xsiny+e^x-3y^2 dx

The solution

You have entered [src]

  1                          
  /                          
 |                           
 |  /            x      2\   
 |  \x*sin(y) + e  - 3*y / dx
 |                           
/                            
0

$$\int\limits_{0}^{1} \left(x \sin{\left(y \right)} - 3 y^{2} + e^{x}\right)\, dx$$

Integral(x*sin(y) + E^x - 3*y^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int x \sin{\left(y \right)}\, dx = \sin{\left(y \right)} \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2} \sin{\left(y \right)}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(- 3 y^{2}\right)\, dx = - 3 x y^{2}$
1. The integral of the exponential function is itself.
  
  $\int e^{x}\, dx = e^{x}$
The result is: $\frac{x^{2} \sin{\left(y \right)}}{2} - 3 x y^{2} + e^{x}$
Now simplify:

$\frac{x^{2} \sin{\left(y \right)}}{2} - 3 x y^{2} + e^{x}$
Add the constant of integration:

$\frac{x^{2} \sin{\left(y \right)}}{2} - 3 x y^{2} + e^{x}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \sin{\left(y \right)}}{2} - 3 x y^{2} + e^{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                       
 |                                       2                
 | /            x      2\           x   x *sin(y)        2
 | \x*sin(y) + e  - 3*y / dx = C + e  + --------- - 3*x*y 
 |                                          2             
/

$${{x^2\,\sin y}\over{2}}-3\,x\,y^2+e^{x}$$

Simplify

The answer [src]

         sin(y)      2
-1 + e + ------ - 3*y 
           2

$${{\sin y-6\,y^2+2\,e-2}\over{2}}$$

         sin(y)      2
-1 + e + ------ - 3*y 
           2

$$- 3 y^{2} + \frac{\sin{\left(y \right)}}{2} - 1 + e$$

Simplify

Use the examples entering the upper and lower limits of integration.

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Integral of u=xsiny+e^x-3y^2 dx

Limits of integration:

The graph:

Piecewise:

The solution