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Exercise 7.2

let I 

Put x+4= t

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Let t

∴2x dx = dt

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Let log |x| = t

∴ 

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Let 1 + log t

∴ 

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sin x ⋅ sin (cos x)

sin x ⋅ sin (cos x)

Let cos x = t

∴ −sin x dx = dt

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Let 

∴ 2adx = dt

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Let ax + b = t

⇒ adx = dt

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Let 

∴ dx = dt

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Let 1 + 2x2 = t

∴ 4xdx = dt

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Integrate the question

Let 

∴ (2x + 1)dx = dt

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Let 

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Let 

∴ 

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Let 

∴ 9x2dx = dt

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Let log x = t

∴ 

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Let 

∴ −8x dx = dt

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Let 

∴ 2dx = dt

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Let 

∴ 2xdx = dt

 

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Let 

∴ 

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Dividing numerator and denominator by ex, we obtain

Let 

∴ 

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Let 

∴ 

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Let 2x − 3 = t

∴ 2dx = dt

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Let 7 − 4x = t

∴ −4dx = dt

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Let 

∴ 

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Let 

∴ 

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Let 

∴ 

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Let 

∴ 

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Let sin 2x = t

∴ 

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Let 

∴ cos x dx = dt

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cot x log sin x

Let log sin x = t

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Let 1 + cos x = t

∴ −sin x dx = dt

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Let sin x + cos x = t ⇒ (cos x − sin xdx = dt

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Put cos x − sin x = t ⇒ (−sin x − cos xdx = dt

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Divide Numerator and Deminator by cos2x

I =

Put tan x = t

sec2x dx = dt

 I  =   

=

=

I =

 

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Let 1 + log x = t

∴ 

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Let 

∴ 

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Let x4 = t

∴ 4x3 dx = dt

Let 

From (1), we obtain

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equals

Let 

∴ 

Hence, the correct answer is D.

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equals

A.

B.

C.

D.

Hence, the correct answer is B.

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