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

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

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integral of 5sin(3x)

\int 5 sin (3 x) d x

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

Solution steps

\int 5 sin (3 x) d x

Take the constant out:

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

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

Apply u-substitution

: \int sin (u) \frac{1}{3} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 3 x

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

Simplify

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

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

Add a constant to the solution

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

y = lo g_{3} (5 x^{4})

2 x^{2} + y^{2} - 7 = 0

\int_{π}^{2 π} - cos (x) d x

x \to 1 lim (\frac{x - x ^{3}}{x - 1})

\frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4}) + cos (x) + 1)