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Solving integrals/ 3*x*sin(y)+1

Integral of 3*x*sin(y)+1 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                    
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 |  (3*x*sin(y) + 1) dx
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0
$$\int\limits_{0}^{1} \left(3 x \sin{\left(y \right)} + 1\right)\, dx$$ 
Integral((3*x)*sin(y) + 1, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 2       
 |                               3*x *sin(y)
 | (3*x*sin(y) + 1) dx = C + x + -----------
 |                                    2     
/
$$\int \left(3 x \sin{\left(y \right)} + 1\right)\, dx = C + \frac{3 x^{2} \sin{\left(y \right)}}{2} + x$$
Simplify
The answer [src] 
    3*sin(y)
1 + --------
       2
$$\frac{3 \sin{\left(y \right)}}{2} + 1$$ 
=
= 
    3*sin(y)
1 + --------
       2
$$\frac{3 \sin{\left(y \right)}}{2} + 1$$ 
1 + 3*sin(y)/2

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

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