What is the integral of (cos(5x)) ?

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

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integral of (cos(5x))

\int (cos (5 x)) d x

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

Solution steps

\int cos (5 x) d x

Apply u-substitution

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

= \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 \int cos (u) d u

Use the common integral:

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

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

Substitute back

u = 5 x

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

Add a constant to the solution

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

\frac{d}{d x} (2^{l n (x)})

y = cos (a^{4} + x^{4})

(7, 5), (- 4, - 1)

\int_{0}^{\frac{π}{4}} sec^{5} (x) d x

f (x) = 8 x^{3} - x^{π}