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Solving integrals/ 5sintcost

Integral of 5sintcost dt

Limits of integration:

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The solution

You have entered [src] 
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 |  5*sin(t*cos(t)) dt
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∫0t5sin⁡(tcos⁡(t)) dt\int\limits_{0}^{t} 5 \sin{\left(t \cos{\left(t \right)} \right)}\, dt 
Integral(5*sin(t*cos(t)), (t, 0, t))
Detail solution

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

    ∫5sin⁡(tcos⁡(t)) dt=5∫sin⁡(tcos⁡(t)) dt\int 5 \sin{\left(t \cos{\left(t \right)} \right)}\, dt = 5 \int \sin{\left(t \cos{\left(t \right)} \right)}\, dt

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

      But the integral is

      ∫sin⁡(tcos⁡(t)) dt\int \sin{\left(t \cos{\left(t \right)} \right)}\, dt

    So, the result is: 5∫sin⁡(tcos⁡(t)) dt5 \int \sin{\left(t \cos{\left(t \right)} \right)}\, dt

  2. Add the constant of integration:

    5∫sin⁡(tcos⁡(t)) dt+constant5 \int \sin{\left(t \cos{\left(t \right)} \right)}\, dt+ \mathrm{constant}

The answer is:

5∫sin⁡(tcos⁡(t)) dt+constant5 \int \sin{\left(t \cos{\left(t \right)} \right)}\, dt+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | 5*sin(t*cos(t)) dt = C + 5* | sin(t*cos(t)) dt
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∫5sin⁡(tcos⁡(t)) dt=C+5∫sin⁡(tcos⁡(t)) dt\int 5 \sin{\left(t \cos{\left(t \right)} \right)}\, dt = C + 5 \int \sin{\left(t \cos{\left(t \right)} \right)}\, dt
Simplify
The answer [src] 
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5* |  sin(t*cos(t)) dt
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5∫0tsin⁡(tcos⁡(t)) dt5 \int\limits_{0}^{t} \sin{\left(t \cos{\left(t \right)} \right)}\, dt 
=
= 
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5* |  sin(t*cos(t)) dt
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  0
5∫0tsin⁡(tcos⁡(t)) dt5 \int\limits_{0}^{t} \sin{\left(t \cos{\left(t \right)} \right)}\, dt 
5*Integral(sin(t*cos(t)), (t, 0, t))

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

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