Integral of log(10)(x) dx

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 |  log(10)*x dx
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$$\int\limits_{0}^{1} x \log{\left(10 \right)}\, dx$$

Integral(log(10)*x, (x, 0, 1))

Detail solution

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

$\int x \log{\left(10 \right)}\, dx = \log{\left(10 \right)} \int x\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
So, the result is: $\frac{x^{2} \log{\left(10 \right)}}{2}$
Add the constant of integration:

$\frac{x^{2} \log{\left(10 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \log{\left(10 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    2        
 |                    x *log(10)
 | log(10)*x dx = C + ----------
 |                        2     
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$$\int x \log{\left(10 \right)}\, dx = C + \frac{x^{2} \log{\left(10 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

log(10)
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   2

$$\frac{\log{\left(10 \right)}}{2}$$

log(10)
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   2

$$\frac{\log{\left(10 \right)}}{2}$$

log(10)/2

Numerical answer [src]

1.15129254649702

1.15129254649702

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