Intégration par parties - 3 exemples (leçon)

Exercice 1

integral, e, start superscript, x, end superscript, ×, sine, x, d, x, equals

(Choix A)
e, start superscript, x, end superscript, ×, left parenthesis, sine, x, plus, cosine, x, right parenthesis, plus, C
(Choix B)
start fraction, 1, divided by, 2, end fraction, e, start superscript, x, end superscript, ×, left parenthesis, sine, x, minus, cosine, x, right parenthesis, plus, C
(Choix C)
2, e, start superscript, x, end superscript, ×, sine, x, plus, C
(Choix D)
start fraction, e, start superscript, x, end superscript, ×, cosine, x, divided by, 2, end fraction, plus, C

integral, left parenthesis, natural log, x, right parenthesis, squared, d, x, equals

(Choix A)
x, ×, left parenthesis, natural log, x, right parenthesis, squared, plus, C
(Choix B)
x, ×, left parenthesis, natural log, x, right parenthesis, squared, minus, 2, natural log, x, plus, C
(Choix C)
x, ×, left parenthesis, natural log, x, right parenthesis, squared, minus, 2, natural log, x, plus, 2, x, plus, C
(Choix D)
x, ×, left parenthesis, natural log, x, right parenthesis, squared, minus, 2, x, ×, natural log, x, plus, 2, x, plus, C

integral, x, squared, ×, sine, left parenthesis, pi, x, right parenthesis, d, x, equals

(Choix A)
start fraction, minus, x, squared, ×, cosine, left parenthesis, pi, x, right parenthesis, plus, x, ×, sine, left parenthesis, pi, x, right parenthesis, divided by, pi, end fraction, plus, start fraction, cosine, left parenthesis, pi, x, right parenthesis, divided by, pi, squared, end fraction, plus, C
(Choix B)
minus, start fraction, x, squared, ×, cosine, left parenthesis, pi, x, right parenthesis, divided by, pi, end fraction, plus, start fraction, 2, x, ×, sine, left parenthesis, pi, x, right parenthesis, divided by, pi, squared, end fraction, plus, start fraction, 2, cosine, left parenthesis, pi, x, right parenthesis, divided by, pi, cubed, end fraction, plus, C
(Choix C)
start fraction, minus, x, squared, ×, cosine, left parenthesis, pi, x, right parenthesis, plus, 2, x, ×, sine, left parenthesis, pi, x, right parenthesis, plus, 2, cosine, left parenthesis, pi, x, right parenthesis, divided by, pi, end fraction, plus, C
(Choix D)
minus, start fraction, x, squared, ×, cosine, left parenthesis, pi, x, right parenthesis, divided by, pi, end fraction, plus, 2, x, ×, sine, left parenthesis, pi, x, right parenthesis, plus, C