What is the integral of 6cos(5x) ?

The integral of 6cos(5x) is 6/5 sin(5x)+C

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integral of 6cos(5x)

\int 6 cos (5 x) d x

\frac{6}{5} sin (5 x) + C

Solution steps

\int 6 cos (5 x) d x

Take the constant out:

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

= 6 \cdot \int cos (5 x) d x

Apply u-substitution

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

= 6 \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

= 6 \cdot \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= 6 \cdot \frac{1}{5} sin (u)

Substitute back

u = 5 x

= 6 \cdot \frac{1}{5} sin (5 x)

Simplify

6 \cdot \frac{1}{5} sin (5 x) : \frac{6}{5} sin (5 x)

= \frac{6}{5} sin (5 x)

Add a constant to the solution

= \frac{6}{5} sin (5 x) + C

y = 2 (x + y) y^{^{'}}

\int 3 sin^{6} (x) cos (x) d x

x \to 0 lim (100)

\frac{d}{d x} (a x^{2} e^{2 x})

h (t) = (t^{\frac{2}{5}} + 3) (3 t^{5} + 5)