What is the integral of sin(4x+5) ?

The integral of sin(4x+5) is -1/4 cos(4x+5)+C

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integral of sin(4x+5)

\int sin (4 x + 5) d x

- \frac{1}{4} cos (4 x + 5) + C

Solution steps

\int sin (4 x + 5) d x

Apply u-substitution

= \int sin (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{4} (- cos (u))

Substitute back

u = 4 x + 5

= \frac{1}{4} (- cos (4 x + 5))

Simplify

= - \frac{1}{4} cos (4 x + 5)

Add a constant to the solution

= - \frac{1}{4} cos (4 x + 5) + C

\int sin^{2} (t) cos^{4} (t) d t

\frac{d}{d x} (\frac{2 x}{( x + 1 )})

\int \frac{2 x + 1}{x ^{2} + 2 x + 5} d x

\int \frac{1}{2} e^{2 x} d x

x y^{^{'}} + 3 y = x^{3} - x

What is the integral of sin(4x+5) ?
The integral of sin(4x+5) is -1/4 cos(4x+5)+C