What is the integral of 2cos(7x-4) ?

The integral of 2cos(7x-4) is 2/7 sin(7x-4)+C

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integral of 2cos(7x-4)

\int 2 cos (7 x - 4) d x

\frac{2}{7} sin (7 x - 4) + C

Solution steps

\int 2 cos (7 x - 4) d x

Take the constant out:

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

= 2 \cdot \int cos (7 x - 4) d x

Apply u-substitution

: \int cos (u) \frac{1}{7} d u

= 2 \cdot \int cos (u) \frac{1}{7} d u

Take the constant out:

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

= 2 \cdot \frac{1}{7} \cdot \int cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{7} sin (u)

Substitute back

u = 7 x - 4

= 2 \cdot \frac{1}{7} sin (7 x - 4)

Simplify

2 \cdot \frac{1}{7} sin (7 x - 4) : \frac{2}{7} sin (7 x - 4)

= \frac{2}{7} sin (7 x - 4)

Add a constant to the solution

= \frac{2}{7} sin (7 x - 4) + C

y^{^{''}} + 9 y = csc^{2} (3 t)

y^{^{'}} = 2 y - t^{2}

\int_{0}^{2} sin (x^{2}) d x

\frac{\partial}{\partial x} (- x y z^{2} + 16)

y = x - x^{3} (1)

What is the integral of 2cos(7x-4) ?
The integral of 2cos(7x-4) is 2/7 sin(7x-4)+C