Integral of (3x+2sinx) dx

The solution

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

Integral(3*x + 2*sin(x), (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:
  
  $\int 3 x\, dx = 3 \int x\, dx$
  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: $\frac{3 x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(x \right)}\, dx = 2 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
The result is: $\frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                        2
 |                                      3*x 
 | (3*x + 2*sin(x)) dx = C - 2*cos(x) + ----
 |                                       2  
/

$$\int \left(3 x + 2 \sin{\left(x \right)}\right)\, dx = C + \frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/2 - 2*cos(1)

$$\frac{7}{2} - 2 \cos{\left(1 \right)}$$

7/2 - 2*cos(1)

$$\frac{7}{2} - 2 \cos{\left(1 \right)}$$

7/2 - 2*cos(1)

Numerical answer [src]

2.41939538826372

2.41939538826372

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

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Integral of (3x+2sinx) dx

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The solution