Mister Exam

Other calculators

Integral of x^4+3sin(3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |  / 4             \   
 |  \x  + 3*sin(3*x)/ dx
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \left(x^{4} + 3 \sin{\left(3 x \right)}\right)\, dx$$
Integral(x^4 + 3*sin(3*x), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of is when :

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

      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:

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                        
 |                                        5
 | / 4             \                     x 
 | \x  + 3*sin(3*x)/ dx = C - cos(3*x) + --
 |                                       5 
/                                          
$$\int \left(x^{4} + 3 \sin{\left(3 x \right)}\right)\, dx = C + \frac{x^{5}}{5} - \cos{\left(3 x \right)}$$
The graph
The answer [src]
6/5 - cos(3)
$$\frac{6}{5} - \cos{\left(3 \right)}$$
=
=
6/5 - cos(3)
$$\frac{6}{5} - \cos{\left(3 \right)}$$
6/5 - cos(3)
Numerical answer [src]
2.18999249660045
2.18999249660045

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