Question

Evaluate the integral.
The integral of the arctan ( 5t) dt

Answer 1

Do you know how to do integration by parts?

Answer 2

yes , im actually stuck . the computer program i have to use ask me to simplify the integral (5t/1+25t^2) dt to the intergral of (?t/1+25t^2)(5/50)dt but i dont know what that number is

Answer 3

\[I=\int\limits \tan^{-1} (5t) dt =\int\limits \tan^{-1} (5t)*1 dt\]
integrate by parts.

Answer 4

\[I=\tan^{-1} (5t)*t-\int\limits \frac{ 5 }{ 1+25t ^{2} }*tdt\]
\[=t* \tan^{-1} (5t)-\frac{ 1 }{10 }\ln (1+25 t ^{2})+c\]

Answer 5

okay thanks

Answer 6

yw