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exp(7*x)*sin(x)
Solving integrals/ exp(7*x)*sin(x)

Integral of exp(7*x)*sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |   7*x          
 |  e   *sin(x) dx
 |                
/                 
0
$$\int\limits_{0}^{1} e^{7 x} \sin{\left(x \right)}\, dx$$ 
Integral(exp(7*x)*sin(x), (x, 0, 1))
Detail solution

  1. Use integration by parts, noting that the integrand eventually repeats itself.

    1. For the integrand :

      Let and let .

      Then .

    2. For the integrand :

      Let and let .

      Then .

    3. Notice that the integrand has repeated itself, so move it to one side:

      Therefore,

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                
 |                              7*x      7*x       
 |  7*x                 cos(x)*e      7*e   *sin(x)
 | e   *sin(x) dx = C - ----------- + -------------
 |                           50             50     
/
$$\int e^{7 x} \sin{\left(x \right)}\, dx = C + \frac{7 e^{7 x} \sin{\left(x \right)}}{50} - \frac{e^{7 x} \cos{\left(x \right)}}{50}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
             7      7       
1    cos(1)*e    7*e *sin(1)
-- - --------- + -----------
50       50           50
$$- \frac{e^{7} \cos{\left(1 \right)}}{50} + \frac{1}{50} + \frac{7 e^{7} \sin{\left(1 \right)}}{50}$$ 
=
= 
             7      7       
1    cos(1)*e    7*e *sin(1)
-- - --------- + -----------
50       50           50
$$- \frac{e^{7} \cos{\left(1 \right)}}{50} + \frac{1}{50} + \frac{7 e^{7} \sin{\left(1 \right)}}{50}$$ 
1/50 - cos(1)*exp(7)/50 + 7*exp(7)*sin(1)/50
Numerical answer [src] 
117.359629247603
117.359629247603
The graph
Integral of exp(7*x)*sin(x) dx

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

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