7.1 inderfinite integral — ગણિત ધોરણ 12 સાયન્સ — Question
Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\log x(\log x + 2)\;dx = } $
✓
$x{(\log x)^2} + c$
B
$x{(1 + \log x)^2} + c$
C
$x[1 + {(\log x)^2}] + c$
D
એકપણ નહિ.
✓
Answer
Correct option: A.
$x{(\log x)^2} + c$
a (a) $I = \int_{}^{} {\log x(\log x + 2)\,dx} $
Put $\log x = t \Rightarrow {e^t} = x \Rightarrow {e^t}dt = dx,$ then
$I = \int_{}^{} {t(t + 2){e^t}dt} = {t^2}.\,{e^t} + c = x{(\log x)^2} + c.$
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