What is the integral of sin(t/3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(t/3)

\int sin (\frac{t}{3}) d t

- 3 cos (\frac{t}{3}) + C

Solution steps

\int sin (\frac{t}{3}) d t

Apply u-substitution

: \int sin (u) \cdot 3 d u

= \int sin (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int sin (u) d u

Use the common integral:

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

= 3 (- cos (u))

Substitute back

u = \frac{t}{3}

= 3 (- cos (\frac{t}{3}))

Simplify

= - 3 cos (\frac{t}{3})

Add a constant to the solution

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

\int (2 x - 1) (x^{2} + 2) d x

\int ln (x^{2} + 3 x) d x

\int (x^{4} - 2 x^{2}) (4 x^{2} - 4) d x

\int 6 \frac{( ln ( z ) ) ^{2}}{z} d z