Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (x+3)e^x
Integral of sinxcos2x
Integral of x/(x^2-5x+4)
Integral of (x+4)/(x^2(x-1))
Identical expressions
(x^ two)sinxx^ three + one
(x squared ) sinus of xx cubed plus 1
(x to the power of two) sinus of xx to the power of three plus one
(x2)sinxx3+1
x2sinxx3+1
(x²)sinxx³+1
(x to the power of 2)sinxx to the power of 3+1
x^2sinxx^3+1
(x^2)sinxx^3+1dx
Similar expressions
(x^2)sinxx^3-1

Integral of (x^2)sinxx^3+1 dx

The solution

You have entered [src]

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

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

Integral((x^2*sin(x))*x^3 + 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- x^{5} \cos{\left(x \right)} + 5 x^{4} \sin{\left(x \right)} + 20 x^{3} \cos{\left(x \right)} - 60 x^{2} \sin{\left(x \right)} - 120 x \cos{\left(x \right)} + 120 \sin{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $- x^{5} \cos{\left(x \right)} + 5 x^{4} \sin{\left(x \right)} + 20 x^{3} \cos{\left(x \right)} - 60 x^{2} \sin{\left(x \right)} - 120 x \cos{\left(x \right)} + x + 120 \sin{\left(x \right)}$
Add the constant of integration:

$- x^{5} \cos{\left(x \right)} + 5 x^{4} \sin{\left(x \right)} + 20 x^{3} \cos{\left(x \right)} - 60 x^{2} \sin{\left(x \right)} - 120 x \cos{\left(x \right)} + x + 120 \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- x^{5} \cos{\left(x \right)} + 5 x^{4} \sin{\left(x \right)} + 20 x^{3} \cos{\left(x \right)} - 60 x^{2} \sin{\left(x \right)} - 120 x \cos{\left(x \right)} + x + 120 \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                                                                 
 |                                                                                                                  
 | / 2         3    \                            5                             2             4              3       
 | \x *sin(x)*x  + 1/ dx = C + x + 120*sin(x) - x *cos(x) - 120*x*cos(x) - 60*x *sin(x) + 5*x *sin(x) + 20*x *cos(x)
 |                                                                                                                  
/

$$\int \left(x^{3} x^{2} \sin{\left(x \right)} + 1\right)\, dx = C - x^{5} \cos{\left(x \right)} + 5 x^{4} \sin{\left(x \right)} + 20 x^{3} \cos{\left(x \right)} - 60 x^{2} \sin{\left(x \right)} - 120 x \cos{\left(x \right)} + x + 120 \sin{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1 - 101*cos(1) + 65*sin(1)

$$- 101 \cos{\left(1 \right)} + 1 + 65 \sin{\left(1 \right)}$$

1 - 101*cos(1) + 65*sin(1)

$$- 101 \cos{\left(1 \right)} + 1 + 65 \sin{\left(1 \right)}$$

1 - 101*cos(1) + 65*sin(1)

Numerical answer [src]

1.12508111983116

1.12508111983116

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x^2)sinxx^3+1 dx

Limits of integration:

The graph:

Piecewise:

The solution