2.3 Übungen

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|width="50%"| <math>\displaystyle\int x \ln x \, dx</math>
|width="50%"| <math>\displaystyle\int x \ln x \, dx</math>
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</div>{{#NAVCONTENT:Svar|Svar 2.3:1|Lösning a|Lösning 2.3:1a|Lösning b|Lösning 2.3:1b|Lösning c|Lösning 2.3:1c|Lösning d|Lösning 2.3:1d}}
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</div>{{#NAVCONTENT:Answer|Svar 2.3:1|Solution a|Lösning 2.3:1a|Solution b|Lösning 2.3:1b|Solution c|Lösning 2.3:1c|Solution d|Lösning 2.3:1d}}
===Exercise 2.3:2===
===Exercise 2.3:2===
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|width="50%"| <math>\displaystyle\int \ln x\, dx</math>
|width="50%"| <math>\displaystyle\int \ln x\, dx</math>
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</div>{{#NAVCONTENT:Svar|Svar 2.3:2|Lösning a|Lösning 2.3:2a|Lösning b|Lösning 2.3:2b|Lösning c|Lösning 2.3:2c|Lösning d|Lösning 2.3:2d}}
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</div>{{#NAVCONTENT:Answer|Svar 2.3:2|Solution a|Lösning 2.3:2a|Solution b|Lösning 2.3:2b|Solution c|Lösning 2.3:2c|Solution d|Lösning 2.3:2d}}

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Exercise 2.3:1

Calculate the integrals

a) \displaystyle \displaystyle\int 2x e^{-x} \, dx b) \displaystyle \displaystyle\int(x+1) \sin x \, dx
c) \displaystyle \displaystyle\int x^2 \cos x \, dx d) \displaystyle \displaystyle\int x \ln x \, dx

Exercise 2.3:2

Calculate the integrals

a) \displaystyle \displaystyle\int e^{\sqrt x}\, dx b) \displaystyle \displaystyle\int_{0}^{1} x^3 e^{x^2} \, dx
c) \displaystyle \displaystyle\int \tan x \, dx d) \displaystyle \displaystyle\int \ln x\, dx