Suppose for and

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Suppose

\dfrac{dy}{dx}=\dfrac{3x^{2}+4}{x^{3}+4x}

for

x>0

and

y(1)=0

. Which of the following gives

y(x)

for

x>0

? (a)

y(x)=\ln\!\left(x^{2}+4\right)-\ln 5

(b)

y(x)=\ln\!\left(\dfrac{x(x^{2}+4)}{5}\right)

(c)

y(x)=\ln\!\left(\dfrac{x^{2}+4}{x}\right)-\ln 5

(d)

y(x)=\dfrac{1}{5}\,\ln\!\left[x(x^{2}+4)\right]

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