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

The integral of (sqrt(t)+1)(t+1) is 2/5 t^{5/2}+2/3 t^{3/2}+(t^2)/2+t+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)+1)(t+1)

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

\frac{2}{5} t^{\frac{5}{2}} + \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2} + t + C

Solution steps

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

Expand

(t + 1) (t + 1) : t^{\frac{3}{2}} + t + t + 1

= \int t^{\frac{3}{2}} + t + t + 1 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

= \int t^{\frac{3}{2}} d t + \int t d t + \int t d t + \int 1 d t

\int t^{\frac{3}{2}} d t = \frac{2}{5} t^{\frac{5}{2}}

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

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

\int 1 d t = t

= \frac{2}{5} t^{\frac{5}{2}} + \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2} + t

Add a constant to the solution

= \frac{2}{5} t^{\frac{5}{2}} + \frac{2}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2} + t + C

\int \frac{1}{sin ^{2} ( 4 θ )} d θ

\int \frac{( sec ^{2} ( ln ( x ) ) )}{x} d x

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

\int x^{- \frac{6}{5}} d x

\int \frac{1}{2} x + 2 d x

What is the integral of (sqrt(t)+1)(t+1) ?
The integral of (sqrt(t)+1)(t+1) is 2/5 t^{5/2}+2/3 t^{3/2}+(t^2)/2+t+C