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

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

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

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

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

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = \frac{7}{x}

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

Simplify

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

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

Add a constant to the solution

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

h \to 0 lim (x^{2} + 2 x + h - 69)

y^{^{'}} (t) = (3 + y) (1 - y), y (0) = 2

y^{^{'}} + 2 y = \frac{1}{x}

\int \frac{4 w - 11}{2 w ^{2} + 7 w - 4} d w

\int_{- 1}^{1} 1 1^{x} d x

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