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e^(3x)(cosx)^2

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  • Integral of d{x}:
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  • Integral of e^u Integral of e^u
  • Integral of ex Integral of ex
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  • Identical expressions

  • e^(3x)(cosx)^ two
  • e to the power of (3x)( co sinus of e of x) squared
  • e to the power of (3x)( co sinus of e of x) to the power of two
  • e(3x)(cosx)2
  • e3xcosx2
  • e^(3x)(cosx)²
  • e to the power of (3x)(cosx) to the power of 2
  • e^3xcosx^2
  • e^(3x)(cosx)^2dx
Solving integrals/ e^(3x)(cosx)^2

Integral of e^(3x)(cosx)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |   3*x    2      
 |  e   *cos (x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} e^{3 x} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(E^(3*x)*cos(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                             
 |                            2     3*x         2     3*x             3*x       
 |  3*x    2             2*sin (x)*e      11*cos (x)*e      2*cos(x)*e   *sin(x)
 | e   *cos (x) dx = C + -------------- + --------------- + --------------------
 |                             39                39                  13         
/
$${{6\,e^{3\,x}\,\sin \left(2\,x\right)+9\,e^{3\,x}\,\cos \left(2\,x \right)+13\,e^{3\,x}}\over{78}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            2     3         2     3             3       
  11   2*sin (1)*e    11*cos (1)*e    2*cos(1)*e *sin(1)
- -- + ------------ + ------------- + ------------------
  39        39              39                13
$${{6\,e^3\,\sin 2+9\,e^3\,\cos 2+13\,e^3}\over{78}}-{{11}\over{39}}$$ 
=
= 
            2     3         2     3             3       
  11   2*sin (1)*e    11*cos (1)*e    2*cos(1)*e *sin(1)
- -- + ------------ + ------------- + ------------------
  39        39              39                13
$$- \frac{11}{39} + \frac{2 e^{3} \sin^{2}{\left(1 \right)}}{39} + \frac{2 e^{3} \sin{\left(1 \right)} \cos{\left(1 \right)}}{13} + \frac{11 e^{3} \cos^{2}{\left(1 \right)}}{39}$$
Simplify
Numerical answer [src] 
3.50599421009002
3.50599421009002
The graph
Integral of e^(3x)(cosx)^2 dx

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

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