What is the integral of-1/5 cos(5x) ?

The integral of-1/5 cos(5x) is -1/25 sin(5x)+C

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integral of-1/5 cos(5x)

\int - \frac{1}{5} cos (5 x) d x

- \frac{1}{25} sin (5 x) + C

Solution steps

\int - \frac{1}{5} cos (5 x) d x

Take the constant out:

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

= - \frac{1}{5} \cdot \int cos (5 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= - \frac{1}{5} \cdot \int cos (u) \frac{1}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{1}{5} \cdot \frac{1}{5} sin (u)

Substitute back

u = 5 x

= - \frac{1}{5} \cdot \frac{1}{5} sin (5 x)

Simplify

- \frac{1}{5} \cdot \frac{1}{5} sin (5 x) : - \frac{1}{25} sin (5 x)

= - \frac{1}{25} sin (5 x)

Add a constant to the solution

= - \frac{1}{25} sin (5 x) + C

\int \frac{( 2 x ^{2} + x + 4 )}{x ^{3} + 4 x ^{2}} d x

\frac{d}{d x} (x^{3} + 6)

y^{'} (x)

13 x y^{^{'}} - 2 y = - \frac{x ^{2}}{y ^{12}}

\frac{d}{d x} (5^{(6 x^{2} - x + 2)})

What is the integral of-1/5 cos(5x) ?
The integral of-1/5 cos(5x) is -1/25 sin(5x)+C