What is the integral of 7/(x^2)cos(3/x) ?

The integral of 7/(x^2)cos(3/x) is -7/3 sin(3/x)+C

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integral of 7/(x^2)cos(3/x)

\int \frac{7}{x ^{2}} cos (\frac{3}{x}) d x

- \frac{7}{3} sin (\frac{3}{x}) + C

Solution steps

\int \frac{7}{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

= 7 \cdot \int \frac{1}{x ^{2}} cos (\frac{3}{x}) d x

Apply u-substitution

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

= 7 \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

= 7 (- \frac{1}{3} \cdot \int cos (u) d u)

Use the common integral:

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

= 7 (- \frac{1}{3} sin (u))

Substitute back

u = \frac{3}{x}

= 7 (- \frac{1}{3} sin (\frac{3}{x}))

Simplify

7 (- \frac{1}{3} sin (\frac{3}{x})) : - \frac{7}{3} sin (\frac{3}{x})

= - \frac{7}{3} sin (\frac{3}{x})

Add a constant to the solution

= - \frac{7}{3} sin (\frac{3}{x}) + C

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What is the integral of 7/(x^2)cos(3/x) ?
The integral of 7/(x^2)cos(3/x) is -7/3 sin(3/x)+C