Mister Exam

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Identical expressions
sin(eight *x)+e^(three *x)
sinus of (8 multiply by x) plus e to the power of (3 multiply by x)
sinus of (eight multiply by x) plus e to the power of (three multiply by x)
sin(8*x)+e(3*x)
sin8*x+e3*x
sin(8x)+e^(3x)
sin(8x)+e(3x)
sin8x+e3x
sin8x+e^3x
sin(8*x)+e^(3*x)dx
Similar expressions
sin(8*x)-e^(3*x)

Integral of sin(8x)+e^(3x) dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |  /            3*x\   
 |  \sin(8*x) + E   / dx
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(e^{3 x} + \sin{\left(8 x \right)}\right)\, dx$$

Integral(sin(8*x) + E^(3*x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Let $u = 3 x$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{e^{u}}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    So, the result is: $\frac{e^{u}}{3}$
  Now substitute $u$ back in:
  
  $\frac{e^{3 x}}{3}$
1. Let $u = 8 x$ .
  
  Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :
  
  $\int \frac{\sin{\left(u \right)}}{8}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{8}$
    1. The integral of sine is negative cosine:
      
      $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
    So, the result is: $- \frac{\cos{\left(u \right)}}{8}$
  Now substitute $u$ back in:
  
  $- \frac{\cos{\left(8 x \right)}}{8}$
The result is: $\frac{e^{3 x}}{3} - \frac{\cos{\left(8 x \right)}}{8}$
Add the constant of integration:

$\frac{e^{3 x}}{3} - \frac{\cos{\left(8 x \right)}}{8}+ \mathrm{constant}$

The answer is:

$\frac{e^{3 x}}{3} - \frac{\cos{\left(8 x \right)}}{8}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                        3*x
 | /            3*x\          cos(8*x)   e   
 | \sin(8*x) + E   / dx = C - -------- + ----
 |                               8        3  
/

$$\int \left(e^{3 x} + \sin{\left(8 x \right)}\right)\, dx = C + \frac{e^{3 x}}{3} - \frac{\cos{\left(8 x \right)}}{8}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                 3
  5    cos(8)   e 
- -- - ------ + --
  24     8      3

$$- \frac{5}{24} - \frac{\cos{\left(8 \right)}}{8} + \frac{e^{3}}{3}$$

                 3
  5    cos(8)   e 
- -- - ------ + --
  24     8      3

$$- \frac{5}{24} - \frac{\cos{\left(8 \right)}}{8} + \frac{e^{3}}{3}$$

-5/24 - cos(8)/8 + exp(3)/3

Numerical answer [src]

6.50503314528863

6.50503314528863

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

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Identical expressions

Similar expressions

Integral of sin(8x)+e^(3x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(8*x)+e^(3*x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of sin(8x)+e^(3x) dx