What is the integral of sin(5x+3) ?

The integral of sin(5x+3) is -1/5 cos(5x+3)+C

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integral of sin(5x+3)

integral

sin (5 x + 3)

- \frac{1}{5} cos (5 x + 3) + C

Solution steps

\int sin (5 x + 3) d x

Apply u-substitution

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

= \int sin (u) \frac{1}{5} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{5} (- cos (u))

Substitute back

u = 5 x + 3

= \frac{1}{5} (- cos (5 x + 3))

Simplify

= - \frac{1}{5} cos (5 x + 3)

Add a constant to the solution

= - \frac{1}{5} cos (5 x + 3) + C

\frac{x ^{2}}{x ^{2} + 5}

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

- x^{2} ln (x)

\frac{x ^{2}}{x ^{2} + 1}

\frac{1}{( x ^{2} + 1 ) ^{3}}

What is the integral of sin(5x+3) ?
The integral of sin(5x+3) is -1/5 cos(5x+3)+C