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Similar expressions
1/x+3x^2+sinx
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Integral of 1/x-3x^2+sinx dx

The solution

You have entered [src]

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

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

Integral(1/x - 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:
  
  $\int \left(- 3 x^{2}\right)\, dx = - \int 3 x^{2}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $x^{3}$
  So, the result is: $- x^{3}$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\log{\left(x \right)}$
The result is: $- x^{3} + \log{\left(x \right)} - \cos{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                   
 |                                                    
 | /  1      2         \           3                  
 | |1*- - 3*x  + sin(x)| dx = C - x  - cos(x) + log(x)
 | \  x                /                              
 |                                                    
/

$$\log x-\cos x-x^3$$

Simplify

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Упростить

Numerical answer [src]

43.5501438281248

43.5501438281248

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

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Integral of 1/x-3x^2+sinx dx

Limits of integration:

The graph:

Piecewise:

The solution