Question

explain integration by substitution method....​

Answer 1

Answer:

In this method of integration by substitution, any given integral is transformed into a simple form of integral by substituting the independent variable by others. Take for example an equation having an independent variable in x, i.e. ∫sin (x3).

Answer 2

$\huge {\boxed {\mathbb {QUESTION}}}$

explain integration by substitution method.

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• $Given \:integral\: is\: transformed\: into a\\ simple \:form \:of\: integral \:by\: substituting\: the\\ independent\: variable\: by\: others$

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$\implies \int\frac{{e} ^{tan-1_x}} {1+{x} ^{2}}$

$\implies Let\:t={tan} ^{-1}x ----(1)$

$\implies dt=(\frac{1}{1+{x}^{2}})dx$

$\implies l=\int ({e} ^{t}) dt$

$\implies {e}^{t} +C -----(2)$

$Substitute \:the\:value\:of\:(1) \:in\:(2)$

$\implies{\boxed {\boxed {l={e} ^{tan-1_x}+C}}}$

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