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10 cards from this deck
Use trigonometric identities to simplify first.
The integral is −cos(x)+C-\cos(x) + C−cos(x)+C.
The identity is sin2θ+cos2θ≡1\sin^2\theta + \cos^2\theta \equiv 1sin2θ+cos2θ≡1.
tan2θ+1≡sec2θ\tan^2\theta + 1 \equiv \sec^2\thetatan2θ+1≡sec2θ.
Integrate as sec2θ−1\sec^2\theta - 1sec2θ−1: tanθ−θ+C\tan\theta - \theta + Ctanθ−θ+C.
Integrate to get −ln∣cos(θ)∣+C-\ln|\cos(\theta)| + C−ln∣cos(θ)∣+C.
Use the identity to get −14cos(2θ)+C-\frac{1}{4} \cos(2\theta) + C−41cos(2θ)+C.
Express as 1−2sin2θ1 - 2\sin^2\theta1−2sin2θ.
Get 12θ+14sin(2θ)+C\frac{1}{2}\theta + \frac{1}{4} \sin(2\theta) + C21θ+41sin(2θ)+C.
It's 12x−18sin(4x)+C\frac{1}{2}x - \frac{1}{8}\sin(4x) + C21x−81sin(4x)+C.
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