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

The integral of cos(sqrt(t)) is 2(sqrt(t)sin(sqrt(t))+cos(sqrt(t)))+C

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integral of cos(sqrt(t))

\int cos (t) d t

2 (t sin (t) + cos (t)) + C

Solution steps

\int cos (t) d t

Apply u-substitution

: \int cos (u) \cdot 2 u d u

= \int cos (u) \cdot 2 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cos (u) u d u

Apply Integration By Parts

: u sin (u) - \int sin (u) d u

= 2 (u sin (u) - \int sin (u) d u)

\int sin (u) d u = - cos (u)

= 2 (u sin (u) - (- cos (u)))

Substitute back

u = t

= 2 (t sin (t) - (- cos (t)))

Simplify

= 2 (t sin (t) + cos (t))

Add a constant to the solution

= 2 (t sin (t) + cos (t)) + C

\int_{- 64}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

\frac{\partial}{\partial y} (x^{3} + 3 x^{2} y - 2 y^{2})

\frac{1}{s ( s ^{2} - 2 s + 2 )}

y^{^{'}} + y + \frac{1}{x} y = \frac{e ^{- x}}{x}

What is the integral of cos(sqrt(t)) ?
The integral of cos(sqrt(t)) is 2(sqrt(t)sin(sqrt(t))+cos(sqrt(t)))+C