What is the integral of 3sin(5x+4) ?

The integral of 3sin(5x+4) is -3/5 cos(5x+4)+C

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integral of 3sin(5x+4)

\int 3 sin (5 x + 4) d x

- \frac{3}{5} cos (5 x + 4) + C

Solution steps

\int 3 sin (5 x + 4) d x

Take the constant out:

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

= 3 \cdot \int sin (5 x + 4) d x

Apply u-substitution

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

= 3 \cdot \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

= 3 \cdot \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{5} (- cos (u))

Substitute back

u = 5 x + 4

= 3 \cdot \frac{1}{5} (- cos (5 x + 4))

Simplify

3 \cdot \frac{1}{5} (- cos (5 x + 4)) : - \frac{3}{5} cos (5 x + 4)

= - \frac{3}{5} cos (5 x + 4)

Add a constant to the solution

= - \frac{3}{5} cos (5 x + 4) + C

\int_{1}^{16} e^{x} d x

y^{^{''}} + 4 y^{^{'}} + 13 y = 3 cos (2 x)

\int \frac{1}{y ^{5}} d y

\int \frac{1}{25 x ^{2} - 9} d x

y^{^{''}} - y = 0, y (0) = 0, y (1) = 1

What is the integral of 3sin(5x+4) ?
The integral of 3sin(5x+4) is -3/5 cos(5x+4)+C