What is the integral of cos(-4x) ?

The integral of cos(-4x) is 1/4 sin(4x)+C

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integral of cos(-4x)

\int cos (- 4 x) d x

\frac{1}{4} sin (4 x) + C

Solution steps

\int cos (- 4 x) d x

Apply u-substitution

: \int - \frac{1}{4} cos (u) d u

= \int - \frac{1}{4} cos (u) d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{1}{4} sin (u)

Substitute back

u = - 4 x

= - \frac{1}{4} sin (- 4 x)

Simplify

- \frac{1}{4} sin (- 4 x) : \frac{1}{4} sin (4 x)

= \frac{1}{4} sin (4 x)

Add a constant to the solution

= \frac{1}{4} sin (4 x) + C

\int \frac{1}{1 + e ^{4 x}} d x

(3 x^{2} - 6 x + 6) e^{x}

\frac{( s + 5 )}{( s ^{2} + 5 s + 6 )}

\int e^{- x} (2 - x) d x

ln (tan (4 x))