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Evaluate: ∫ E Tan − 1 X 1 + X 2 D X - Mathematics

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प्रश्न

Evaluate:\[\int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]

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उत्तर

\[\text{ Let I} = \int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]
\[\text{ Let } \tan^{- 1} x = t\]
\[ \Rightarrow \frac{dx}{1 + x^2} = dt\]
\[ \therefore I = \int e^t dt\]
\[ = e^t + C\]
\[ = e^{{tan}^{- 1}} x + C\]

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अध्याय 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९८]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Very Short Answers | Q 50 | पृष्ठ १९८

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