Mister Exam

# Integral of dz÷(5z+tan(y-3x)) dx

from to

from to

### The solution

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  1
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|          1
|  ------------------ dz
|  5*z + tan(y - 3*x)
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0                        
$$\int\limits_{0}^{1} \frac{1}{5 z + \tan{\left(- 3 x + y \right)}}\, dz$$
Integral(1/(5*z + tan(y - 3*x)), (z, 0, 1))
Detail solution
1. Let .

Then let and substitute :

1. The integral of a constant times a function is the constant times the integral of the function:

1. The integral of is .

So, the result is:

Now substitute back in:

2. Now simplify:

3. Add the constant of integration:

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|         1                   log(5*z + tan(y - 3*x))
| ------------------ dz = C + -----------------------
| 5*z + tan(y - 3*x)                     5
|
/                                                     
$$\int \frac{1}{5 z + \tan{\left(- 3 x + y \right)}}\, dz = C + \frac{\log{\left(5 z + \tan{\left(- 3 x + y \right)} \right)}}{5}$$
  log(-tan(-y + 3*x))   log(5 - tan(-y + 3*x))
- ------------------- + ----------------------
5                      5           
$$\frac{\log{\left(5 - \tan{\left(3 x - y \right)} \right)}}{5} - \frac{\log{\left(- \tan{\left(3 x - y \right)} \right)}}{5}$$
=
=
  log(-tan(-y + 3*x))   log(5 - tan(-y + 3*x))
- ------------------- + ----------------------
5                      5           
$$\frac{\log{\left(5 - \tan{\left(3 x - y \right)} \right)}}{5} - \frac{\log{\left(- \tan{\left(3 x - y \right)} \right)}}{5}$$
-log(-tan(-y + 3*x))/5 + log(5 - tan(-y + 3*x))/5

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

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