What is the integral of sin(a-x) ?

The integral of sin(a-x) is cos(a-x)+C

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integral of sin(a-x)

\int sin (a - x) d x

cos (a - x) + C

Solution steps

\int sin (a - x) d x

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

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

= - \int sin (u) d u

Use the common integral:

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

= - (- cos (u))

Substitute back

u = a - x

= - (- cos (a - x))

Simplify

= cos (a - x)

Add a constant to the solution

= cos (a - x) + C

x \to 2 lim (\frac{( x + 3 )}{x + 4})

\frac{d}{d t} (t sin (π t))

\int \frac{1}{t ^{2}} cos (\frac{1}{t} - 1) d t

y = \frac{4}{x ^{5}}

f (x) = 2 x^{3} ln (x)