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

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

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integral of 7/(θ^2)cos(7/θ)

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

- sin (\frac{7}{θ}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 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}{θ}

= 7 (- \frac{1}{7} sin (\frac{7}{θ}))

Simplify

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

= - sin (\frac{7}{θ})

Add a constant to the solution

= - sin (\frac{7}{θ}) + C

\frac{\partial}{\partial x} (1 - \frac{1}{x})

\frac{1}{8 x}

y = x, (25, 5)

f (x) = x + \frac{7}{x}

x \to 0 lim (7^{x})

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