Math Help - Integral of vector function

1. Integral of vector function

Can someone check my work?

$\int_{0}^{1}\left(\frac{4}{1+t^2}\overrightarrow{j }+\frac{2t}{1+t^2}\overrightarrow{k}\right) dt=$

$\left[(4tan^{-1}t) \overrightarrow{j}+ln(1+t^2) \overrightarrow{k}\right]_{0}^{1}=$

$\pi \overrightarrow{j}+ln(2) \overrightarrow{k}$

2. Re: Integral of vector function

That looks right