What is the integral of sqrt(t)cos(t) ?

The integral of sqrt(t)cos(t) is sqrt(t)sin(t)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(t))+C

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integral of sqrt(t)cos(t)

\int t cos (t) d t

t sin (t) - \frac{π}{2} § (\frac{2}{π} t) + C

Solution steps

\int t cos (t) d t

Apply Integration By Parts

: t sin (t) - \int \frac{sin ( t )}{2 t} d t

= t sin (t) - \int \frac{sin ( t )}{2 t} d t

\int \frac{sin ( t )}{2 t} d t = \frac{π}{2} § (\frac{2}{π} t)

= t sin (t) - \frac{π}{2} § (\frac{2}{π} t)

Add a constant to the solution

= t sin (t) - \frac{π}{2} § (\frac{2}{π} t) + C

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What is the integral of sqrt(t)cos(t) ?
The integral of sqrt(t)cos(t) is sqrt(t)sin(t)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(t))+C