Mister Exam

Other calculators

Solving integrals/ e^x*cos3x

Integral of e^x*cos3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |   x            
 |  E *cos(3*x) dx
 |                
/                 
0
$$\int\limits_{0}^{1} e^{x} \cos{\left(3 x \right)}\, dx$$ 
Integral(E^x*cos(3*x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                
 |                                x      x         
 |  x                   cos(3*x)*e    3*e *sin(3*x)
 | E *cos(3*x) dx = C + ----------- + -------------
 |                           10             10     
/
$$\int e^{x} \cos{\left(3 x \right)}\, dx = C + \frac{3 e^{x} \sin{\left(3 x \right)}}{10} + \frac{e^{x} \cos{\left(3 x \right)}}{10}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1    E*cos(3)   3*E*sin(3)
- -- + -------- + ----------
  10      10          10
$$\frac{e \cos{\left(3 \right)}}{10} - \frac{1}{10} + \frac{3 e \sin{\left(3 \right)}}{10}$$ 
=
= 
  1    E*cos(3)   3*E*sin(3)
- -- + -------- + ----------
  10      10          10
$$\frac{e \cos{\left(3 \right)}}{10} - \frac{1}{10} + \frac{3 e \sin{\left(3 \right)}}{10}$$ 
-1/10 + E*cos(3)/10 + 3*E*sin(3)/10
Numerical answer [src] 
-0.25402667531964
-0.25402667531964

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

    © Mister Exam – Calculator