The antiderivative $\int 4 \sec ^ { 2 } x d x$ is

A) $\int 4 \sec ^ { 2 } x d x$
B) $\frac { 4 ( \tan x ) ^ { 3 } } { 3 } + C$
C) $2 ( \tan x ) ^ { 2 } + C$
D) $2 ( \sec x ) ^ { 2 } + C$
E) $4 \tan x + C$

Question

The antiderivative $\int 4 \sec ^ { 2 } x d x$ is

A) $\int 4 \sec ^ { 2 } x d x$
B) $\frac { 4 ( \tan x ) ^ { 3 } } { 3 } + C$
C) $2 ( \tan x ) ^ { 2 } + C$
D) $2 ( \sec x ) ^ { 2 } + C$
E) $4 \tan x + C$

Quizplus · Accepted Answer

The antiderivative of $4 \sec^2 x$ is $4 \tan x + C$, because the derivative of $\tan x$ is $\sec^2 x$, and thus integrating $4 \sec^2 x$ gives $4 \tan x + C$.

The Antiderivative ∫4sec⁡2xdx\int 4 \sec ^ { 2 } x d x∫4sec2xdx

The Antiderivative $\int 4 \sec ^ { 2 } x d x$