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Integral of d{x}:
Integral of xln^2x
Integral of sqrt(sinx)
Integral of dx/8-4sinx+7cosx
Integral of y=2log(2x+1)
Identical expressions
dx/ eight -4sinx+7cosx
dx divide by 8 minus 4 sinus of x plus 7 co sinus of e of x
dx divide by eight minus 4 sinus of x plus 7 co sinus of e of x
dx divide by 8-4sinx+7cosx
Similar expressions
dx/8-4sinx-7cosx
dx/8+4sinx+7cosx

Solving integrals/ dx/8-4sinx+7cosx

Integral of dx/8-4sinx+7cosx dx

The solution

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  1                               
  /                               
 |                                
 |  /  1                      \   
 |  |1*- - 4*sin(x) + 7*cos(x)| dx
 |  \  8                      /   
 |                                
/                                 
0

$$\int\limits_{0}^{1} \left(- 4 \sin{\left(x \right)} + 7 \cos{\left(x \right)} + 1 \cdot \frac{1}{8}\right)\, dx$$

Integral(1/8 - 4*sin(x) + 7*cos(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:
  
  $\int \left(- 4 \sin{\left(x \right)}\right)\, dx = - \int 4 \sin{\left(x \right)}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 4 \sin{\left(x \right)}\, dx = 4 \int \sin{\left(x \right)}\, dx$
    1. The integral of sine is negative cosine:
      
      $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
    So, the result is: $- 4 \cos{\left(x \right)}$
  So, the result is: $4 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 7 \cos{\left(x \right)}\, dx = 7 \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $7 \sin{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1 \cdot \frac{1}{8}\, dx = \frac{x}{8}$
The result is: $\frac{x}{8} + 7 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{x}{8} + 7 \sin{\left(x \right)} + 4 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x}{8} + 7 \sin{\left(x \right)} + 4 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                            
 |                                                             
 | /  1                      \                                x
 | |1*- - 4*sin(x) + 7*cos(x)| dx = C + 4*cos(x) + 7*sin(x) + -
 | \  8                      /                                8
 |                                                             
/

$$7\,\sin x+4\,\cos x+{{x}\over{8}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-31/8 + 4*cos(1) + 7*sin(1)

$${{56\,\sin 1+32\,\cos 1-31}\over{8}}$$

-31/8 + 4*cos(1) + 7*sin(1)

$$- \frac{31}{8} + 4 \cos{\left(1 \right)} + 7 \sin{\left(1 \right)}$$

Упростить

Numerical answer [src]

4.17650611712783

4.17650611712783

The graph

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

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Integral of dx/8-4sinx+7cosx dx

Limits of integration:

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Piecewise:

The solution