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2x^(-3)+3sin(x)
Solving integrals/ 2x^(-3)+3sin(x)

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

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The solution

You have entered [src] 
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 |  /2            \   
 |  |-- + 3*sin(x)| dx
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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
Simplify
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=3∫sin⁡(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:

      ∫2x3 dx=2∫1x3 dx\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 n≠−1n \neq -1:

        ∫1x3 dx=−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           
 | \x            /          x            
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−3 cos⁡x−1x2-3\,\cos x-{{1}\over{x^2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902000000000000-1000000000000
Plot the graph f(x)
The answer [src] 
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∞\infty 
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∞\infty
Simplify
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.

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