Question

integrate sec²(4x)dx​

Answer 1

Answer:

{tan(4x)}/4

is the answer

Answer 2

Answer:

$\frac{1}{4} tan(4x) \: is \: the \: answer.$

Explanation:

$put \: 4x = t \\ differentiating \: on \: both \: sides \: w.r.t \: \\ 4dx = dt \\ dx = \frac{1}{4} dt$

$\int \: {sec}^{2} (4x)dx = \int {sec}^{2} t. \frac{1}{4} dt \\ = \frac{1}{4} \int \: {sec}^{2} t \: dt\\ = \frac{1}{4} tant \\ = \frac{1}{4} tan(4x)$