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Lt(1)/(x rarr3)(1)/(x-3)int(3)^(x)e^(t)d...

Lt(1)/(x rarr3)(1)/(x-3)int_(3)^(x)e^(t)dt

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Lt_(x rarr3)((1)/(x-3)int_(3)^(x)e^(t)dt)=

{:(" "Lt),(x rarr 3):} (1)/(x-3) int_(3)^(x)e^(t)dt=

lim_(x rarr0)((1)/(x^(5))int_(0)^(x)e^(-t^(2))dt-(1)/(x^(4))+(1)/(3x^(2)))

lim_(x rarr0)(1)/(x^(3))int_(0)^(x)(t ln(1+t))/(t^(4)+4)backslash dt

Find the value of Lim_(x rarr 0) (1)/(x^(3)) int_(0)^(x) (t(ln (1+t)))/(t^(4) + 4)dt

The values of lim_(x rarr 0) (1)/(x^(3)) int_(0)^(x) (t In (1 + t))/(t^(4) + 4)dt is :

{:(" " Lt),(x rarr0):}(int_(0)^(x) sin^(3) t dt)/(x^(4))=

{:(" " Lt),(x rarr 0):} (int_(0)^(x^(2))sec^(2) t dt)/(x sin x) =

Lt_(x rarr0)((int_(0)^(x)tan^(2)t sec^(2)tdt)/(x^(3)))=