Mister Exam

Other calculators

Solving integrals/ dz/5z+tan(y-3x)

Integral of dz/5z+tan(y-3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                          
  /                          
 |                           
 |  (0.2*z + tan(y - 3*x)) dz
 |                           
/                            
0
$$\int\limits_{0}^{1} \left(0.2 z + \tan{\left(- 3 x + y \right)}\right)\, dz$$ 
Integral(0.2*z + tan(y - 3*x), (z, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of is when :

      So, the result is:

    1. Rewrite the integrand:

    2. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                        
 |                                      2   z*sin(-y + 3*x)
 | (0.2*z + tan(y - 3*x)) dz = C + 0.1*z  - ---------------
 |                                           cos(-y + 3*x) 
/
$$\int \left(0.2 z + \tan{\left(- 3 x + y \right)}\right)\, dz = C + 0.1 z^{2} - \frac{z \sin{\left(3 x - y \right)}}{\cos{\left(3 x - y \right)}}$$
Simplify
The answer [src] 
0.1 - 1.0*tan(-y + 3*x)
$$0.1 - 1.0 \tan{\left(3 x - y \right)}$$ 
=
= 
0.1 - 1.0*tan(-y + 3*x)
$$0.1 - 1.0 \tan{\left(3 x - y \right)}$$ 
0.1 - 1.0*tan(-y + 3*x)

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

    © Mister Exam – Calculator