What is the integral of cos(4u) ?

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

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integral of cos(4u)

\int cos (4 u) d u

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

Solution steps

\int cos (4 u) d u

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

v = 4 u

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

Add a constant to the solution

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

t an g e n t x^{2} + x y + 2 y^{2} = 28, (- 5, 3)

in v erse l a pl a ce \frac{100}{s ( s ^{2} + 25 )}

x \to 2 - lim (2 x - 4)

x \to 0 lim (\frac{cos ( x )}{2})

\int s d s