What is the integral of sin(7x-10) ?

The integral of sin(7x-10) is -1/7 cos(7x-10)+C

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integral of sin(7x-10)

\int sin (7 x - 10) d x

- \frac{1}{7} cos (7 x - 10) + C

Solution steps

\int sin (7 x - 10) d x

Apply u-substitution

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

= \int sin (u) \frac{1}{7} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{7} (- cos (u))

Substitute back

u = 7 x - 10

= \frac{1}{7} (- cos (7 x - 10))

Simplify

= - \frac{1}{7} cos (7 x - 10)

Add a constant to the solution

= - \frac{1}{7} cos (7 x - 10) + C

x \to \infty lim (4 x^{3})

\frac{d}{d x} (12 x^{3})

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))

\frac{d}{d x} (\frac{4}{9} x^{3})

x sin (x^{2})

What is the integral of sin(7x-10) ?
The integral of sin(7x-10) is -1/7 cos(7x-10)+C