What is the integral of 3/(x^2)cos(3/x) ?

The integral of 3/(x^2)cos(3/x) is -sin(3/x)+C

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integral of 3/(x^2)cos(3/x)

\int \frac{3}{x ^{2}} cos (\frac{3}{x}) d x

- sin (\frac{3}{x}) + C

Solution steps

\int \frac{3}{x ^{2}} cos (\frac{3}{x}) d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{x ^{2}} cos (\frac{3}{x}) d x

Apply u-substitution

: \int - \frac{cos ( u )}{3} d u

= 3 \cdot \int - \frac{cos ( u )}{3} d u

Take the constant out:

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

= 3 (- \frac{1}{3} \cdot \int cos (u) d u)

Use the common integral:

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

= 3 (- \frac{1}{3} sin (u))

Substitute back

u = \frac{3}{x}

= 3 (- \frac{1}{3} sin (\frac{3}{x}))

Simplify

3 (- \frac{1}{3} sin (\frac{3}{x})) : - sin (\frac{3}{x})

= - sin (\frac{3}{x})

Add a constant to the solution

= - sin (\frac{3}{x}) + C

\frac{1}{s ^{3} + 6 s ^{2} + 9 s}

\int \frac{3}{10 - t} d t

\int 35 arctan (x) d x

7 (x^{2} + y^{2}) d x + 8 x y d y = 0

x \to 0 - lim (\frac{cos ( x )}{x})

What is the integral of 3/(x^2)cos(3/x) ?
The integral of 3/(x^2)cos(3/x) is -sin(3/x)+C