What is the integral of 45(1+sqrt(t)) ?

The integral of 45(1+sqrt(t)) is 45(t+2/3 t^{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 45(1+sqrt(t))

\int 45 (1 + t) d t

45 (t + \frac{2}{3} t^{\frac{3}{2}}) + C

Solution steps

\int 45 (1 + t) d t

Take the constant out:

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

= 45 \cdot \int 1 + t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 45 (\int 1 d t + \int t d t)

\int 1 d t = t

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

= 45 (t + \frac{2}{3} t^{\frac{3}{2}})

Add a constant to the solution

= 45 (t + \frac{2}{3} t^{\frac{3}{2}}) + C

\int 5 x^{2} 4 x^{3} + 7 d x

\int \frac{8}{3} x d x

\int 4 x^{\frac{5}{2}} d x

\int x ln (e^{x}) d x

\int x^{2} arctan (d) x d x

What is the integral of 45(1+sqrt(t)) ?
The integral of 45(1+sqrt(t)) is 45(t+2/3 t^{3/2})+C