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MaxKov1995
@MaxKov1995
July 2022
1
16
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Вычислить неопределенный интеграл:
а) ∫(3x^3-4x+8x^4+5)dx; б) ∫(e^x+3^x)dx; в) ∫((√x^3)+x-1/x)dx
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dydx
А) int(3x^3-4x+8x^4+5)dx=
int(3x^3)dx - 4int(x)dx + 8int*x^4)dx+5int(dx)=
(3x^4)/4 - 2x^2 + (8x^5)/5 + 5x + C
б) int(e^x + 3^x)dx = int(e^x)dx + int(3^x)dx =
e^x + (3^x)/ln(3) + C
в) int(x^(3/2) + x - 1/x)dx =
int(x^(3/2))dx +int(x)dx - int(1/x)dx =
x^(2,5)/2,5 + x^2/2 - lnx + C
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Answers & Comments
int(3x^3)dx - 4int(x)dx + 8int*x^4)dx+5int(dx)=
(3x^4)/4 - 2x^2 + (8x^5)/5 + 5x + C
б) int(e^x + 3^x)dx = int(e^x)dx + int(3^x)dx =
e^x + (3^x)/ln(3) + C
в) int(x^(3/2) + x - 1/x)dx =
int(x^(3/2))dx +int(x)dx - int(1/x)dx =
x^(2,5)/2,5 + x^2/2 - lnx + C