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MHT-CET : Mathematics Entrance Exam

MHT - CET : Mathematics - Indefinite Integrals Formulae Page 1

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Integration by parts

1.

If 'u' and 'v' are derivable functions of 'x', then

dx = uv -

dx

2.

If f(x) and g(x) are derivable functions of 'x',
then
f(x). g ' (x) dx = f(x) g(x) - f ' (x) g(x) dx

3.

If 'u' and 'v' are derivable functions of 'x', then

uv dx = u v dx - [( v dx )

du

dx

] dx

4.

If f(x) and g(x) are derivable functions of 'x', then
f(x) g(x) dx = f(x) g(x) dx - [ g(x) dx] f ' (x) dx

5.

If f(x) is a derivable functions of 'x', then
ex [ f(x)+ f ' (x) ] dx = ex f(x) + c

6.

7.

8.

 

Reduction Formulae

1.

sinn dx =

- cos x . sin n - 1 x

n

+

n - 1

n

sinn-2 x dx

2.

cosnx dx =

sin x . cos n - 1 x

n

+

n - 1

n

cosn-2 x dx

 

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