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Identical expressions
(x+ five)*arctgxdx
(x plus 5) multiply by arctgxdx
(x plus five) multiply by arctgxdx
(x+5)arctgxdx
x+5arctgxdx
Similar expressions
(x-5)*arctgxdx

Integral of (x+5)*arctgxdx dx

The solution

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  1                   
  /                   
 |                    
 |  (x + 5)*acot(x) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x + 5\right) \operatorname{acot}{\left(x \right)}\, dx$$

Integral((x + 5)*acot(x), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x + 5\right) \operatorname{acot}{\left(x \right)} = x \operatorname{acot}{\left(x \right)} + 5 \operatorname{acot}{\left(x \right)}$
Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + \frac{x}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 \operatorname{acot}{\left(x \right)}\, dx = 5 \int \operatorname{acot}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $x \operatorname{acot}{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}$
  So, the result is: $5 x \operatorname{acot}{\left(x \right)} + \frac{5 \log{\left(x^{2} + 1 \right)}}{2}$
The result is: $\frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + 5 x \operatorname{acot}{\left(x \right)} + \frac{x}{2} + \frac{5 \log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + 5 x \operatorname{acot}{\left(x \right)} + \frac{x}{2} + \frac{5 \log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + 5 x \operatorname{acot}{\left(x \right)} + \frac{x}{2} + \frac{5 \log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            /     2\    2                      
 |                          x   acot(x)   5*log\1 + x /   x *acot(x)              
 | (x + 5)*acot(x) dx = C + - + ------- + ------------- + ---------- + 5*x*acot(x)
 |                          2      2            2             2                   
/

$$\int \left(x + 5\right) \operatorname{acot}{\left(x \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + 5 x \operatorname{acot}{\left(x \right)} + \frac{x}{2} + \frac{5 \log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   5*log(2)   5*pi
- + -------- + ----
2      2        4

$$\frac{1}{2} + \frac{5 \log{\left(2 \right)}}{2} + \frac{5 \pi}{4}$$

1   5*log(2)   5*pi
- + -------- + ----
2      2        4

$$\frac{1}{2} + \frac{5 \log{\left(2 \right)}}{2} + \frac{5 \pi}{4}$$

1/2 + 5*log(2)/2 + 5*pi/4

Numerical answer [src]

6.1598587683871

6.1598587683871

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

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Identical expressions

Similar expressions

Integral of (x+5)*arctgxdx dx

Limits of integration:

The graph:

Piecewise:

The solution