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Question 1141352: integrate sec^2x dx
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! integral of sec^2 (x) dx = integral of 1/cos^2 (x) dx =
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((sin^2 (x) + cos^2 (x))/cos^2 (x)) dx
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I used the identity sin^2 (x) + cos^2 (x) = 1
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Note the derivative of sin(x)/cos(x) = ((cos(x) * cos(x) - sin(x) * -sin(x))/cos^2 (x)) dx = ((cos^2 (x)+ sin^2 (x))/cos^2 (x)) dx = (1/cos^2 (x)) dx = sec^2 (x) dx
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let u = tan(x) = sin(x)/cos(x)
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du = (1/cos^2 (x)) dx, then
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integral of sec^2 (x) dx = integral of u du = u = tan(x) +constant
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