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2x^(-3)+3sin(x)

Integral of 2x^(-3)+3sin(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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01(3sin(x)+2x3)dx\int\limits_{0}^{1} \left(3 \sin{\left(x \right)} + \frac{2}{x^{3}}\right)\, dx
Detail solution
  1. Integrate term-by-term:

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

      3sin(x)dx=3sin(x)dx\int 3 \sin{\left(x \right)}\, dx = 3 \int \sin{\left(x \right)}\, dx

      1. The integral of sine is negative cosine:

        sin(x)dx=cos(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

      So, the result is: 3cos(x)- 3 \cos{\left(x \right)}

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

      2x3dx=21x3dx\int \frac{2}{x^{3}}\, dx = 2 \int \frac{1}{x^{3}}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

        1x3dx=12x2\int \frac{1}{x^{3}}\, dx = - \frac{1}{2 x^{2}}

      So, the result is: 1x2- \frac{1}{x^{2}}

    The result is: 3cos(x)1x2- 3 \cos{\left(x \right)} - \frac{1}{x^{2}}

  2. Add the constant of integration:

    3cos(x)1x2+constant- 3 \cos{\left(x \right)} - \frac{1}{x^{2}}+ \mathrm{constant}


The answer is:

3cos(x)1x2+constant- 3 \cos{\left(x \right)} - \frac{1}{x^{2}}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                      
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 | /2            \          1            
 | |-- + 3*sin(x)| dx = C - -- - 3*cos(x)
 | | 3           |           2           
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3cosx1x2-3\,\cos x-{{1}\over{x^2}}
The graph
0.001.000.100.200.300.400.500.600.700.800.902000000000000-1000000000000
The answer [src]
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Numerical answer [src]
1.83073007580698e+38
1.83073007580698e+38
The graph
Integral of 2x^(-3)+3sin(x) dx

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