ex17-18-19-20.mw

> Exercice 17

> Int((4*t^2-5*t+2)*exp(-t),t)=int((4*t^2-5*t+2)*exp(-t),t);

Int((4*t^2-5*t+2)*exp(-t), t) = -(5+3*t+4*t^2)*exp(-t)

> Int(exp(t)*cos(4*t),t)=int(exp(t)*cos(4*t),t);

Int(exp(t)*cos(4*t), t) = 1/17*exp(t)*cos(4*t)+4/17*exp(t)*sin(4*t)

> Int((t^3-t^2+2*t-3)*sin(t),t)=int((t^3-t^2+2*t-3)*sin(t),t);

Int((t^3-t^2+2*t-3)*sin(t), t) = -cos(t)*t^3+3*sin(t)*t^2-4*sin(t)+4*cos(t)*t+cos(t)*t^2+cos(t)-2*sin(t)*t

> Int(t^3*sin(t),t)=int(t^3*sin(t),t);

Int(t^3*sin(t), t) = -cos(t)*t^3+3*sin(t)*t^2-6*sin(t)+6*cos(t)*t

> Int(t^3*cos(t),t)=int(t^3*cos(t),t);

Int(cos(t)*t^3, t) = t^3*sin(t)+3*cos(t)*t^2-6*cos(t)-6*sin(t)*t

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> Exercice 18

> Int(1/(a^2-t^2),t)=int(1/(a^2-t^2),t);

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Int(1/(a^2-t^2), t) = 1/2*ln(t+a)/a-1/2*ln(t-a)/a

> Int(1/sqrt(a^2-t^2),t)=int(1/sqrt(a^2-t^2),t);

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Int(1/(a^2-t^2)^(1/2), t) = arctan(t/(a^2-t^2)^(1/2))

> Int(1/sqrt(a^2+t^2),t)=int(1/sqrt(a^2+t^2),t);

Int(1/(a^2+t^2)^(1/2), t) = ln(t+(a^2+t^2)^(1/2))

> Int(1/sqrt(t^2-a^2),t)=int(1/sqrt(t^2-a^2),t);

Int(1/(-a^2+t^2)^(1/2), t) = ln(t+(-a^2+t^2)^(1/2))

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> Exercice 19

> Int(1/sqrt(2*t^2-t-5),t)=int(1/sqrt(2*t^2-t-5),t);

Int(1/(2*t^2-t-5)^(1/2), t) = 1/2*ln(1/2*(-1/2+2*t)*2^(1/2)+(2*t^2-t-5)^(1/2))*2^(1/2)

> Int(1/((1+t^2)*sqrt(1-t^2)),t=0..sqrt(2)/2)=int(1/((1+t^2)*sqrt(1-t^2)),t=0..sqrt(2)/2);

Int(1/((1+t^2)*(1-t^2)^(1/2)), t = 0 .. 1/2*2^(1/2)) = 1/2*arctan(2^(1/2))*2^(1/2)

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> Exercice 20

> Int(1/sin(t),t)=int(1/sin(t),t);

Int(1/sin(t), t) = ln(csc(t)-cot(t))

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