What is the integral of (t+5)^2sqrt(3-t) ?

The integral of (t+5)^2sqrt(3-t) is -2/7 (-t+3)^{7/2}+32/5 (-t+3)^{5/2}-128/3 (-t+3)^{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 (t+5)^2sqrt(3-t)

\int (t + 5)^{2} 3 - t d t

- \frac{2}{7} (- t + 3)^{\frac{7}{2}} + \frac{32}{5} (- t + 3)^{\frac{5}{2}} - \frac{128}{3} (- t + 3)^{\frac{3}{2}} + C

Solution steps

\int (t + 5)^{2} 3 - t d t

Expand

(t + 5)^{2} 3 - t : t^{2} 3 - t + 10 t 3 - t + 25 3 - t

= \int t^{2} 3 - t + 10 t 3 - t + 25 3 - 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

= \int t^{2} 3 - t d t + \int 10 t 3 - t d t + \int 25 3 - t d t

\int t^{2} 3 - t d t = - \frac{2}{7} (3 - t)^{\frac{7}{2}} + \frac{12}{5} (3 - t)^{\frac{5}{2}} - 6 (3 - t)^{\frac{3}{2}}

\int 10 t 3 - t d t = - 10 (- \frac{2}{5} (3 - t)^{\frac{5}{2}} + 2 (3 - t)^{\frac{3}{2}})

\int 25 3 - t d t = - \frac{50}{3} (3 - t)^{\frac{3}{2}}

= - \frac{2}{7} (3 - t)^{\frac{7}{2}} + \frac{12}{5} (3 - t)^{\frac{5}{2}} - 6 (3 - t)^{\frac{3}{2}} - 10 (- \frac{2}{5} (3 - t)^{\frac{5}{2}} + 2 (3 - t)^{\frac{3}{2}}) - \frac{50}{3} (3 - t)^{\frac{3}{2}}

Simplify

- \frac{2}{7} (3 - t)^{\frac{7}{2}} + \frac{12}{5} (3 - t)^{\frac{5}{2}} - 6 (3 - t)^{\frac{3}{2}} - 10 (- \frac{2}{5} (3 - t)^{\frac{5}{2}} + 2 (3 - t)^{\frac{3}{2}}) - \frac{50}{3} (3 - t)^{\frac{3}{2}} : - \frac{2}{7} (- t + 3)^{\frac{7}{2}} + \frac{32}{5} (- t + 3)^{\frac{5}{2}} - \frac{128}{3} (- t + 3)^{\frac{3}{2}}

= - \frac{2}{7} (- t + 3)^{\frac{7}{2}} + \frac{32}{5} (- t + 3)^{\frac{5}{2}} - \frac{128}{3} (- t + 3)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{7} (- t + 3)^{\frac{7}{2}} + \frac{32}{5} (- t + 3)^{\frac{5}{2}} - \frac{128}{3} (- t + 3)^{\frac{3}{2}} + C

\int 4 cos (t) sin (t) d t

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

\int \frac{x}{cos ( x ) + 1} d x

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

\int \frac{x + 8}{x ^{2} + 3 x} d x

What is the integral of (t+5)^2sqrt(3-t) ?
The integral of (t+5)^2sqrt(3-t) is -2/7 (-t+3)^{7/2}+32/5 (-t+3)^{5/2}-128/3 (-t+3)^{3/2}+C