Question

Find ∫sec^3xtanxdx

A sin2x+c

B cos2x+c

C sec3x3+c

D cos3x+c

Answer 1

Answer on Question #50928, Math, Integral Calculus

Find $f\sec^3 x\tan xdx$

A $\sin 2x + c$

B $\cos 2x + c$

C $\sec 3x + c$

D $\cos 3x + c$

Answer:

$$\int \sec^3 x \cdot \tan x \, dx = \int \frac{1}{\cos^3 x} \frac{\sin x}{\cos x} \, dx = - \int \frac{1}{\cos^4 x} \, d \cos x = \frac{1}{3} \frac{1}{\cos^3 x} + c = \frac{\sec^3 x}{3} + c$$

The answer C is close to

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