∫ sec(2x)tan(2x)dx
i got 1/cos(2x)
calculator gives me 1/(2cos(2x))
2007-08-04 10:50:26 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
∫(1/cos2x * sin2x /cos2x) dx
∫sin2x /cos^2(2x) dx
Let, u = cos2x
du = -2sin2x dx
-du/2 = sin2x dx
∫-du/2u^2
= 1/2u + c
= 1/2cos(2x) + c
yep the calculator is right
2007-08-04 11:04:58 · answer #1 · answered by Anonymous · 1⤊ 0⤋
â«(1/cos2x * sin2x /cos2x) dx
â«sin2x /cos^2(2x) dx
Again make a substitution,
Let, u = cos2x
du = -2sin2x dx
-du/2 = sin2x dx
â«-du/2u^2
= 1/2u + c
= 1/2cos(2x) + c
Again u made a small mistake while substituting.
2007-08-04 17:55:16 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The calculator is correct. A factor of 1/2 emerges, due to the chain rule.
2007-08-04 17:54:39 · answer #3 · answered by lithiumdeuteride 7 · 0⤊ 0⤋