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y=4cosx+sin3x−8x.

Integral of y=4cosx+sin3x−8x. dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src]
  1                               
  /                               
 |                                
 |  (4*cos(x) + sin(3*x) - 8*x) dx
 |                                
/                                 
0                                 
$$\int\limits_{0}^{1} \left(- 8 x + \sin{\left(3 x \right)} + 4 \cos{\left(x \right)}\right)\, dx$$
Integral(4*cos(x) + sin(3*x) - 8*x, (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. Let .

      Then let and substitute :

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

        1. The integral of sine is negative cosine:

        So, the result is:

      Now substitute back in:

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

      1. The integral of cosine is sine:

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                               
 |                                         2              cos(3*x)
 | (4*cos(x) + sin(3*x) - 8*x) dx = C - 4*x  + 4*sin(x) - --------
 |                                                           3    
/                                                                 
$$-{{\cos \left(3\,x\right)}\over{3}}+4\,\sin x-4\,x^2$$
The graph
The answer [src]
  11              cos(3)
- -- + 4*sin(1) - ------
  3                 3   
$$-{{\cos 3-12\,\sin 1+11}\over{3}}$$
=
=
  11              cos(3)
- -- + 4*sin(1) - ------
  3                 3   
$$- \frac{11}{3} - \frac{\cos{\left(3 \right)}}{3} + 4 \sin{\left(1 \right)}$$
Numerical answer [src]
0.0292147714317345
0.0292147714317345
The graph
Integral of y=4cosx+sin3x−8x. dx

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