What is the integral of 2tsqrt(t) ?

The integral of 2tsqrt(t) is 4/5 t^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2tsqrt(t)

\int 2 t t d t

\frac{4}{5} t^{\frac{5}{2}} + C

Solution steps

\int 2 t t d t

Take the constant out:

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

= 2 \cdot \int t t d t

Simplify

t t : t^{\frac{3}{2}}

= 2 \cdot \int t^{\frac{3}{2}} d t

Apply the Power Rule

= 2 \cdot \frac{2}{5} t^{\frac{5}{2}}

Simplify

2 \cdot \frac{2}{5} t^{\frac{5}{2}} : \frac{4}{5} t^{\frac{5}{2}}

= \frac{4}{5} t^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{5} t^{\frac{5}{2}} + C