Provocare integrarea prin părți (articol)

Problema 1

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

(Varianta A)
e, start superscript, x, end superscript, left parenthesis, sine, x, plus, cosine, x, right parenthesis, plus, C
(Varianta 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
(Varianta C)
2, e, start superscript, x, end superscript, sine, x, plus, C
(Varianta 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

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

(Varianta 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
(Varianta 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
(Varianta 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
(Varianta 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