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

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,

$\int\Big(\dfrac{5}{2}x^{\frac{3}{2}}+8x\Big)dx$

$=x^{\frac{5}{2}}+4x^2+C$