## Homework Statement

$$\int$$ arctan4t dt

## The Attempt at a Solution

ive been attempting this all day. the answer is t arctan4t-1/8 ln(1+16t^2)+C

i get this asnwer up until the 1/8.......

a few steps befor emy answer i have t arctan4t - $$\int$$ 4t/ 1+16t^2

Mark44
Mentor

In your last integral, there's a fairly obvious substitution.

BTW, you need more parentheses: the integrand can be written more understandably as 4t/(1 + 16t^2)

what would be the substituition? in the book after thsi they factor out a 1/8......im lost

Dick
Homework Helper

Substitute u=1+16t^2.

??? so am i integrating by parts again?

Dick
Homework Helper

??? so am i integrating by parts again?
No, it's a u substitution.

i finnaly got it. this textbook sucks at explaining this. thanks guys. sorry dick i was confused at first cause u said let u= 16x^2+1 and i already used u. i get what you were saying now and it makes alot of sense. thanks!