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

Integral of (2/sin^2x-3e^x) dx

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The solution

You have entered [src] 
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 |  /   2         x\   
 |  |------- - 3*e | dx
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∫01(−3ex+2sin⁡2(x)) dx\int\limits_{0}^{1} \left(- 3 e^{x} + \frac{2}{\sin^{2}{\left(x \right)}}\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:

      ∫(−3ex) dx=−∫3ex dx\int \left(- 3 e^{x}\right)\, dx = - \int 3 e^{x}\, dx

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

        ∫3ex dx=3∫ex dx\int 3 e^{x}\, dx = 3 \int e^{x}\, dx

        1. The integral of the exponential function is itself.

          ∫ex dx=ex\int e^{x}\, dx = e^{x}

        So, the result is: 3ex3 e^{x}

      So, the result is: −3ex- 3 e^{x}

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

      ∫2sin⁡2(x) dx=2∫1sin⁡2(x) dx\int \frac{2}{\sin^{2}{\left(x \right)}}\, dx = 2 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx

      1. Don't know the steps in finding this integral.

        But the integral is

        −cos⁡(x)sin⁡(x)- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

      So, the result is: −2cos⁡(x)sin⁡(x)- \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}

    The result is: −3ex−2cos⁡(x)sin⁡(x)- 3 e^{x} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}

  2. Now simplify:

    −3ex−2tan⁡(x)- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}

  3. Add the constant of integration:

    −3ex−2tan⁡(x)+constant- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer is:

−3ex−2tan⁡(x)+constant- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                         
 |                                          
 | /   2         x\             x   2*cos(x)
 | |------- - 3*e | dx = C - 3*e  - --------
 | |   2          |                  sin(x) 
 | \sin (x)       /                         
 |                                          
/
−2tan⁡x−3 ex-{{2}\over{\tan x}}-3\,e^{x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90200000000-100000000
Plot the graph f(x)
The answer [src] 
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Simplify
Numerical answer [src] 
2.75864735589719e+19
2.75864735589719e+19
The graph
Integral of (2/sin^2x-3e^x) dx

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

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