What is the integral of sqrt(t)sin(2t^{3/2}) ?

The integral of sqrt(t)sin(2t^{3/2}) is -1/3 cos(2t^{3/2})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(t)sin(2t^{3/2})

\int t sin (2 t^{\frac{3}{2}}) d t

- \frac{1}{3} cos (2 t^{\frac{3}{2}}) + C

Solution steps

\int t sin (2 t^{\frac{3}{2}}) d t

Apply u-substitution

: \int 2 u^{2} sin (2 u^{3}) d u

= \int 2 u^{2} sin (2 u^{3}) d u

Take the constant out:

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

= 2 \cdot \int u^{2} sin (2 u^{3}) d u

Apply u-substitution

: \int \frac{sin ( v )}{6} d v

= 2 \cdot \int \frac{sin ( v )}{6} d v

Take the constant out:

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

= 2 \cdot \frac{1}{6} \cdot \int sin (v) d v

Use the common integral:

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

= 2 \cdot \frac{1}{6} (- cos (v))

Substitute back

= 2 \cdot \frac{1}{6} (- cos (2 (t)^{3}))

Simplify

2 \cdot \frac{1}{6} (- cos (2 (t)^{3})) : - \frac{1}{3} cos (2 t^{\frac{3}{2}})

= - \frac{1}{3} cos (2 t^{\frac{3}{2}})

Add a constant to the solution

= - \frac{1}{3} cos (2 t^{\frac{3}{2}}) + C

\int t^{t} d t

\int π^{x} + π^{π} + x^{π} d x

\int x e^{\frac{- x}{3}} d x

\int \frac{20}{x} + 3 cos (x) d x

\int y e^{- \frac{y}{2}} d y

What is the integral of sqrt(t)sin(2t^{3/2}) ?
The integral of sqrt(t)sin(2t^{3/2}) is -1/3 cos(2t^{3/2})+C