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sin^6x*cosxdx
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sin6x*cosxdx
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sin^6xcosxdx
sin6xcosxdx

Solving integrals/ sin^6x*cosxdx

Integral of sin^6x*cosxdx dx

The solution

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  1                  
  /                  
 |                   
 |     6             
 |  sin (x)*cos(x) dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(sin(x)^6*cos(x), (x, 0, 1))

Detail solution

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

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

$\int u^{6}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{6}\, du = \frac{u^{7}}{7}$
Now substitute $u$ back in:

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

$\frac{\sin^{7}{\left(x \right)}}{7}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{7}{\left(x \right)}}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                            7   
 |    6                    sin (x)
 | sin (x)*cos(x) dx = C + -------
 |                            7   
/

$$\int \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{7}{\left(x \right)}}{7}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   7   
sin (1)
-------
   7

$$\frac{\sin^{7}{\left(1 \right)}}{7}$$

   7   
sin (1)
-------
   7

$$\frac{\sin^{7}{\left(1 \right)}}{7}$$

sin(1)^7/7

Numerical answer [src]

0.0426752405751304

0.0426752405751304

The graph

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

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Identical expressions

Integral of sin^6x*cosxdx dx

Limits of integration:

The graph:

Piecewise:

The solution