Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x²+4
Integral of x/(raiz(2x-5))
Integral of x^3e^x
Integral of (x+1)/(x^2+2x-1)
x^7*cos(y)
Identical expressions
x^ seven *cos(y)
x to the power of 7 multiply by co sinus of e of (y)
x to the power of seven multiply by co sinus of e of (y)
x7*cos(y)
x7*cosy
x⁷*cos(y)
x^7cos(y)
x7cos(y)
x7cosy
x^7cosy
x^7*cos(y)dx

Integral of x^7*cos(y) dx

The solution

You have entered [src]

 x - 4*cos(y)            
       /                 
      |                  
      |       7          
      |      x *cos(y) dx
      |                  
     /                   
     0

$$\int\limits_{0}^{x - 4 \cos{\left(y \right)}} x^{7} \cos{\left(y \right)}\, dx$$

Integral(x^7*cos(y), (x, 0, x - 4*cos(y)))

Detail solution

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

$\int x^{7} \cos{\left(y \right)}\, dx = \cos{\left(y \right)} \int x^{7}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{7}\, dx = \frac{x^{8}}{8}$
So, the result is: $\frac{x^{8} \cos{\left(y \right)}}{8}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                     8       
 |  7                 x *cos(y)
 | x *cos(y) dx = C + ---------
 |                        8    
/

$$\int x^{7} \cos{\left(y \right)}\, dx = C + \frac{x^{8} \cos{\left(y \right)}}{8}$$

Simplify

The answer [src]

              8       
(x - 4*cos(y)) *cos(y)
----------------------
          8

$$\frac{\left(x - 4 \cos{\left(y \right)}\right)^{8} \cos{\left(y \right)}}{8}$$

              8       
(x - 4*cos(y)) *cos(y)
----------------------
          8

$$\frac{\left(x - 4 \cos{\left(y \right)}\right)^{8} \cos{\left(y \right)}}{8}$$

(x - 4*cos(y))^8*cos(y)/8

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

Other calculators

How to use it?

Identical expressions

Integral of x^7*cos(y) dx

Limits of integration:

The graph:

Piecewise:

The solution