integrale

1
Tabelul Integralelor Integrarea prin parti : f(x)g’(x)dx=f(x)g(x)- f’(x)g(x)dx + + = + c a x dx x a a 1 1 + + = + c a u dx u u a a 1 1 / + = c x dx x 2 1 + = c u dx u u 2 / + = - c x n dx x n n n 1 1 + = - c u n dx u u n n n 1 / c a a dx a x x + = ln c a a dx a u u u + = ln / c e dx e x x + = c e dx e u u u + = / c x dx x + = ln 1 + = c u dx u u ln / = xdx sin -cos x +c c u udx u + - = cos sin / c x dx x + = sin cos c u udx u + = sin cos / c x tgxdx + - = cos ln c u tgudx u + - = cos ln / c x ctgxdx + = sin ln c u ctgudx u + = sin ln / c a x dx x a + = - arcsin 1 2 2 + = - c a u dx u a u arcsin 2 2 / + - + = - c a x x dx a x 2 2 2 2 ln 1 c a u u dx a u u + - + = - 2 2 2 2 / ln + + - = - c a x a x a dx a x ln 2 1 1 2 2 + + - = - c a u a u a dx a u u ln 2 1 2 2 / + = + c a x arctg a dx a x 1 1 2 2 + = + c a u arctg a dx a u u 1 2 2 / ( 29 + + + = + c a x x dx a x 2 2 2 2 ln 1 ( 29 + + + = + c a u u dx a u u 2 2 2 2 / ln + - = c x dx x 1 1 2 + - = c u dx u u 1 2 / + = c x tg dx x 2 ln sin 1 + = c u tg dx u u 2 ln sin / + - = c ctgx dx x 2 sin 1 + - = c ctgu dx x u 2 / sin + = c tgx dx x 2 cos 1 c tgu dx u u + = 2 / cos

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integrale

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Page 1: Integrale

Tabelul Integralelor

Integrarea prin parti : ∫ f(x)g’(x)dx=f(x)g(x)- ∫ f’(x)g(x)dx

∫ ++

=+

ca

xdxx

aa

1

1

∫ ++

=+

ca

udxuu

aa

1

1/

∫ += cxdxx

21

∫ += cudxu

u2

/

∫ +=−

cxndxx

n

n n 1

1∫ +=

−cundx

u

u n

n n 1

/

ca

adxa

xx +=∫ ln

ca

adxau

uu +=∫ ln

/

cedxe xx +=∫ cedxeu uu +=∫ /

cxdxx

+=∫ ln1

∫ += cudxu

uln

/

=∫ xdxsin -cos x +c cuudxu +−=∫ cossin/

cxdxx +=∫ sincos cuudxu +=∫ sincos/

cxtgxdx +−=∫ cosln cutgudxu +−=∫ cosln/

cxctgxdx +=∫ sinln cuctgudxu +=∫ sinln/

ca

xdx

xa+=

−∫ arcsin1

22 ∫ +=−

ca

udx

ua

uarcsin

22

/

∫ +−+=−

caxxdxax

22

22ln

1cauudx

au

u +−+=−∫ 22

22

/

ln

∫ ++−=

−c

ax

ax

adx

axln

2

1122 ∫ +

+−=

−c

au

au

adx

au

uln

2

122

/

∫ +=+

ca

xarctga

dxax

1122 ∫ +=

+c

a

uarctga

dxau

u 122

/

( )∫ +++=+

caxxdxax

22

22ln

1 ( )∫ +++=+

cauudxau

u 22

22

/

ln

∫ +−= cx

dxx

112 ∫ +−= c

udx

u

u 12

/

∫ += cx

tgdxx 2

lnsin

1∫ += c

utgdx

u

u

2ln

sin

/

∫ +−= cctgxdxx2sin

1∫ +−= cctgudx

x

u2

/

sin

∫ += ctgxdxx2cos

1ctgudx

u

u +=∫ 2

/

cos