Let for . What is…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

K(x)=\displaystyle\int_{x}^{\ln x} \dfrac{\tan t}{t}\,dt

for

x>1

. What is

K'(x)

? (a)

-\dfrac{\tan(\ln x)}{x\ln x}+\dfrac{\tan x}{x}

(b)

\dfrac{\tan(\ln x)}{x\ln x}-\dfrac{\tan x}{x}

(c)

\dfrac{\tan(\ln x)}{\ln x}-\dfrac{\tan x}{x}

(d)

\dfrac{\tan(\ln x)}{x\ln x}+\dfrac{\tan x}{x}