Mister Exam

Other calculators


exp(x)*cos(x)^2*x

You entered:

exp(x)*cos(x)^2*x

What you mean?

Integral of exp(x)*cos(x)^2*x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |   x    2        
 |  e *cos (x)*x dx
 |                 
/                  
0                  
$$\int\limits_{0}^{1} x e^{x} \cos^{2}{\left(x \right)}\, dx$$
Integral(exp(x)*cos(x)^2*x, (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                                                                                 
 |                             2     x         2     x             x                 2     x          2     x               x       
 |  x    2               14*sin (x)*e    11*cos (x)*e    4*cos(x)*e *sin(x)   2*x*sin (x)*e    3*x*cos (x)*e    2*x*cos(x)*e *sin(x)
 | e *cos (x)*x dx = C - ------------- - ------------- - ------------------ + -------------- + -------------- + --------------------
 |                             25              25                25                 5                5                   5          
/                                                                                                                                   
$${{\left(10\,x-4\right)\,e^{x}\,\sin \left(2\,x\right)+\left(5\,x+3 \right)\,e^{x}\,\cos \left(2\,x\right)+\left(25\,x-25\right)\,e^{x} }\over{50}}$$
The graph
The answer [src]
            2             2                       
11   4*e*sin (1)   4*e*cos (1)   6*e*cos(1)*sin(1)
-- - ----------- + ----------- + -----------------
25        25            25               25       
$${{3\,e\,\sin 2+4\,e\,\cos 2}\over{25}}+{{11}\over{25}}$$
=
=
            2             2                       
11   4*e*sin (1)   4*e*cos (1)   6*e*cos(1)*sin(1)
-- - ----------- + ----------- + -----------------
25        25            25               25       
$$- \frac{4 e \sin^{2}{\left(1 \right)}}{25} + \frac{4 e \cos^{2}{\left(1 \right)}}{25} + \frac{6 e \sin{\left(1 \right)} \cos{\left(1 \right)}}{25} + \frac{11}{25}$$
Numerical answer [src]
0.555614499239488
0.555614499239488
The graph
Integral of exp(x)*cos(x)^2*x dx

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