$\"\"$

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(a)

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The integral is $\"\"$ .

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Here Integration by parts need not be used.

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The integral is in the form of $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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(b)

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The integral is $\"\"$ .

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Formula for integration by parts: $\"\"$ .

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Here consider $\"\"$ and $\"\"$

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consider $\"\"$ .

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Differentiate with respect to $\"\"$ on each side.

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$\"\"$

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Consider $\"\"$ .

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Find $\"\"$ by integrating $\"\"$ .

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$\"\"$

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$\"\"$

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Susbtitute all the values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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(c)

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The integral is $\"\"$ .

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Formula for integration by parts: $\"\"$ .

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Here consider $\"\"$ and $\"\"$

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And $\"\"$ and $\"\"$ .

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$\"\"$

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(d)

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The integral is $\"\"$ .

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Here Integration by parts need not be used.

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Solve the integral using substitution method.

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Here consider $\"\"$ and $\"\"$ .

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And $\"\"$ . $\"\"$

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(e)

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The integral is $\"\"$ .

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Formula for integration by parts: $\"\"$ .

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Here consider $\"\"$ and $\"\"$ .

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And $\"\"$ and $\"\"$ . $\"\"$

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(f)

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The integral is $\"\"$ .

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Here Integration by parts need not be used.

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Solve the integral using substitution method.

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Here consider $\"\"$ and $\"\"$ .

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And $\"\"$ and $\"\"$ . $\"\"$

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(a) $\"\"$ and $\"\"$ .

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(b) $\"\"$ and $\"\"$ .

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(c) $\"\"$ and $\"\"$ .

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(d) $\"\"$ and $\"\"$ .

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(e) $\"\"$ and $\"\"$ .

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(f) $\"\"$ and $\"\"$ .