Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(-x^3)
Integral of (x^2)
Integral of |x|+1dx
Integral of dx/(3*x-7)
Identical expressions
x*sin(x^ two + one)
x multiply by sinus of (x squared plus 1)
x multiply by sinus of (x to the power of two plus one)
x*sin(x2+1)
x*sinx2+1
x*sin(x²+1)
x*sin(x to the power of 2+1)
xsin(x^2+1)
xsin(x2+1)
xsinx2+1
xsinx^2+1
x*sin(x^2+1)dx
Similar expressions
x*sin(x^2-1)

Solving integrals/ x*sin(x^2+1)

Integral of x*sin(x^2+1) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |       / 2    \   
 |  x*sin\x  + 1/ dx
 |                  
/                   
0

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

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

Detail solution

Let $u = x^{2} + 1$ .

Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\sin{\left(u \right)}}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{2}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{2}$
Now substitute $u$ back in:

$- \frac{\cos{\left(x^{2} + 1 \right)}}{2}$
Now simplify:

$- \frac{\cos{\left(x^{2} + 1 \right)}}{2}$
Add the constant of integration:

$- \frac{\cos{\left(x^{2} + 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(x^{2} + 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                           / 2    \
 |      / 2    \          cos\x  + 1/
 | x*sin\x  + 1/ dx = C - -----------
 |                             2     
/

$$\int x \sin{\left(x^{2} + 1 \right)}\, dx = C - \frac{\cos{\left(x^{2} + 1 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

cos(1)   cos(2)
------ - ------
  2        2

$$- \frac{\cos{\left(2 \right)}}{2} + \frac{\cos{\left(1 \right)}}{2}$$

cos(1)   cos(2)
------ - ------
  2        2

$$- \frac{\cos{\left(2 \right)}}{2} + \frac{\cos{\left(1 \right)}}{2}$$

cos(1)/2 - cos(2)/2

Numerical answer [src]

0.478224571207641

0.478224571207641

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x*sin(x^2+1) dx

Limits of integration:

The graph:

Piecewise:

The solution