Tính nguyên hàm của hàm số
a. y = 1- x
b. y = 2 + x2
c. y = x3 – 9
d. y = 2/5 + 1/3×x2
e. y = (1/2)×căn x – 1/x2
f. y = 5/2 ×x mũ 3/2 + 8x
Tính nguyên hàm của hàm số a. y = 1- x b. y = 2 + x2 c. y = x3 – 9 d. y = 2/5 + 1/3×x2 e. y = (1/2)×căn x – 1/x2 f. y = 5/2 ×x mũ 3/2 + 8x
By Harper
Giải thích các bước giải:
a.$\int 1-xdx=x-\dfrac{x^2}{2}+C$
b.$\int 2+x^2dx=2x+\dfrac{x^2}{2} +C$
c.$\int x^3-9dx=\dfrac{x^4}{4}-9x+C$
d.$\int \dfrac{2}{5}+\dfrac{1}{3}.x^2dx=\dfrac{2x}{5}+\dfrac{x^3}{9}+C$
e.$\int \dfrac{1}{2}\sqrt{x}-\dfrac{1}{x^2}dx$
$=\dfrac{1}{3}.x^{\dfrac{3}{2}}+\dfrac{1}{x}+C$
f.$\int\dfrac{5}{2}.x^{\dfrac{3}{2}}+8xdx$
$=x^{\dfrac{5}{2}}+4x^2+C$
a,
$\int(1-x)dx= x-\dfrac{1}{2}x^2+C$
b,
$\int(2+x^2)dx= 2x+\dfrac{x^3}{3}+C$
c,
$\int(x^3-9)dx=\dfrac{x^4}{4}-9x+C$
d,
$\int\Big(\dfrac{2}{5}+\dfrac{1}{3}x^2\Big)dx$
$=\dfrac{2}{5}x+\dfrac{x^3}{9}+C$
e,
$\int\Big( \dfrac{1}{2}\sqrt{x}-\dfrac{1}{x^2}\Big)dx$
$=\int\Big(\dfrac{1}{2}x^{\frac{1}{2}}-\dfrac{1}{x^2}\Big)dx$
$=\dfrac{1}{3}x^{\frac{3}{2}}+\dfrac{1}{x}+C$
f,
$\int\Big(\dfrac{5}{2}x^{\frac{3}{2}}+8x\Big)dx$
$=x^{\frac{5}{2}}+4x^2+C$