What is the integral of cos(2/t) ?

The integral of cos(2/t) is tcos(2/t)+2\Si(2/t)+C

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integral of cos(2/t)

integral

cos (\frac{2}{t})

t cos (\frac{2}{t}) + 2 Si (\frac{2}{t}) + C

Solution steps

\int cos (\frac{2}{t}) d t

Apply u-substitution

: \int - \frac{2 cos ( u )}{u ^{2}} d u

= \int - \frac{2 cos ( u )}{u ^{2}} d u

Take the constant out:

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

= - 2 \cdot \int \frac{cos ( u )}{u ^{2}} d u

Apply Integration By Parts

: - \frac{cos ( u )}{u} - \int \frac{sin ( u )}{u} d u

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

\int \frac{sin ( u )}{u} d u = Si (u)

= - 2 (- \frac{cos ( u )}{u} - Si (u))

Substitute back

u = \frac{2}{t}

= - 2 (- \frac{cos ( \frac{2}{t} )}{\frac{2}{t}} - Si (\frac{2}{t}))

Simplify

- 2 (- \frac{cos ( \frac{2}{t} )}{\frac{2}{t}} - Si (\frac{2}{t})) : t cos (\frac{2}{t}) + 2 Si (\frac{2}{t})

= t cos (\frac{2}{t}) + 2 Si (\frac{2}{t})

Add a constant to the solution

= t cos (\frac{2}{t}) + 2 Si (\frac{2}{t}) + C

arctan (x^{2})

\frac{( e ^{- x} ) ^{2}}{b}

5 t^{2} - t

\frac{1}{ln ^{2} ( x )}

x csc^{5} (x^{2})

What is the integral of cos(2/t) ?
The integral of cos(2/t) is tcos(2/t)+2\Si(2/t)+C