Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*sin(x)^2
Integral of x²+2x
Integral of (x^2+2x)
Integral of x/(16x^4+1)
Identical expressions
seven ^cos*sinx
7 to the power of co sinus of e of multiply by sinus of x
seven to the power of co sinus of e of multiply by sinus of x
7cos*sinx
7^cossinx
7cossinx
7^cos*sinxdx

Integral of 7^cos*sinx dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |   cos(x)          
 |  7      *sin(x) dx
 |                   
/                    
0

$$\int\limits_{0}^{1} 7^{\cos{\left(x \right)}} \sin{\left(x \right)}\, dx$$

Integral(7^cos(x)*sin(x), (x, 0, 1))

Detail solution

Let $u = \cos{\left(x \right)}$ .

Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :

$\int \left(- 7^{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 7^{u}\, du = - \int 7^{u}\, du$
  1. The integral of an exponential function is itself divided by the natural logarithm of the base.
    
    $\int 7^{u}\, du = \frac{7^{u}}{\log{\left(7 \right)}}$
  So, the result is: $- \frac{7^{u}}{\log{\left(7 \right)}}$
Now substitute $u$ back in:

$- \frac{7^{\cos{\left(x \right)}}}{\log{\left(7 \right)}}$
Add the constant of integration:

$- \frac{7^{\cos{\left(x \right)}}}{\log{\left(7 \right)}}+ \mathrm{constant}$

The answer is:

$- \frac{7^{\cos{\left(x \right)}}}{\log{\left(7 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                          cos(x)
 |  cos(x)                 7      
 | 7      *sin(x) dx = C - -------
 |                          log(7)
/

$$\int 7^{\cos{\left(x \right)}} \sin{\left(x \right)}\, dx = - \frac{7^{\cos{\left(x \right)}}}{\log{\left(7 \right)}} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          cos(1)
  7      7      
------ - -------
log(7)    log(7)

$$- \frac{7^{\cos{\left(1 \right)}}}{\log{\left(7 \right)}} + \frac{7}{\log{\left(7 \right)}}$$

          cos(1)
  7      7      
------ - -------
log(7)    log(7)

$$- \frac{7^{\cos{\left(1 \right)}}}{\log{\left(7 \right)}} + \frac{7}{\log{\left(7 \right)}}$$

7/log(7) - 7^cos(1)/log(7)

Numerical answer [src]

2.12671861830105

2.12671861830105

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

Other calculators

How to use it?

Identical expressions

Integral of 7^cos*sinx dx

Limits of integration:

The graph:

Piecewise:

The solution