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MTH112: Calculus II-2025SPRG-LECT-02

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integral fraction numerator ln left parenthesis ln x right parenthesis over denominator x space ln x end fraction d x equals integral u space d u

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Evaluate the following integral

integral e to the power of x space end exponent c o t h open parentheses e to the power of x close parentheses d x

 

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integral tan x space ln left parenthesis s e c x right parenthesis space d x equals integral u space d u

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Evaluate the following integral 

integral space fraction numerator open parentheses sin x minus cos x close parentheses over denominator open parentheses 1 plus cos x plus sin x close parentheses end fraction d x

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Evaluate the following integral

integral fraction numerator 1 over denominator square root of x squared plus 2 x end root end fraction d x

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Evaluate the following integral

integral 2 to the power of begin display style 1 over x end style end exponent over x squared d x

 

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Evaluate the following integral

integral fraction numerator s e c squared x over denominator square root of 4 minus tan squared x end root end fraction d x

 

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Evaluate the following integral 

integral space fraction numerator open parentheses sin x minus cos x close parentheses over denominator open parentheses cos x plus sin x close parentheses end fraction d x

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Evaluate the following integral

integral fraction numerator sin square root of x over denominator square root of x space cos cubed open parentheses square root of x close parentheses end root end fraction d x

 

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integral fraction numerator e to the power of x over denominator 4 plus e to the power of 2 x end exponent end fraction d xequals integral fraction numerator 1 over denominator 4 plus u squared end fraction space d u

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