Integration by parts MIDTERM really quick question

[banfill_89]

integration by parts! MIDTERM...really quick question...please help!

Homework Statement

$$\int$$ arctan4t dt

Homework Equations

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

i don't kno whow to go from here to the answer...someone please help!

 

[Mark44]

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)

 

[banfill_89]

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

 

[Dick]

Substitute u=1+16t^2.

 

[banfill_89]

? so am i integrating by parts again?

 

[Dick]

? so am i integrating by parts again?

No, it's a u substitution.

 

[banfill_89]

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 a lot of sense. thanks!