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

Popular >

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

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

= 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

\int \frac{x ^{2}}{( x ^{3} + 1 ) ^{7}} d x

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

\int \frac{1}{( 3 x ) ^{2}} + 3 d x

\int - \frac{54}{x ^{15}} d x

\int e^{x} (1 - \frac{e ^{- x}}{x}) d x