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

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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

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