u(x) = xu′(x) = 1 v′(x) = ex v(x) = ex I = ∫ x ×ex dx = [x ·ex ]7 1−∫ 1

N. 7. ſu(x) = x u'(x) = 1. | v'(x) = ek v(x) = e*. 1= xx e*dx=(xe" || -1x e*dx = 6:e'. J1 rt t. {le = " - 1=[ **ë dx=(*-1-). | u(x) = x u'(x) = 1. | v'(x) = e* v(x) = e*. I = 1 x x e* dx.
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(

u(x) = x

(

u(x) = x

(

u(x) = ln (x)

v ′ (x) = e x

v ′ (x) = e x

u ′ (x) = 1 v(x) = e x

u ′ (x) = 1 v(x) = e x

u ′ (x) = (x)−1

v ′ (x) = 1 v(x) = x Ipp([undef]);

I=

Z7

I=

Zt

1

1

i7 Z7 h 1 × ex d x = 6 · e7 x × ex d x = x · ex − 1

x

h

x ×e dx = x ·e

I=

Zt 1

x

it

1

1

−

Zt 1

¡ ¢ 1 × ex d x = t · et − et

it Z t h ln (x) × 1d x = x · ln (x) − (x)−1 × xd x = t · ln (t ) − t + 1 1

1

1