Lời giải:
\(=-\int ^5_2\frac{x^4+3x^2-4}{x^2-1}dx=-\int ^5_2\frac{(x^2-1)(x^2+4)}{x^2-1}dx=-\int ^5_2(x^2+4)dx\)
\(=-|^5_2(\frac{x^3}{3}+4x)=-51\)
Tính nguyên hàm của:
1, \(\int\)\(\dfrac{x^3}{x-2}dx\)
2, \(\int\)\(\dfrac{dx}{x\sqrt{x^2+1}}\)
3, \(\int\)\((\dfrac{5}{x}+\sqrt{x^3})dx\)
4, \(\int\)\(\dfrac{x\sqrt{x}+\sqrt{x}}{x^2}dx\)
5, \(\int\)\(\dfrac{dx}{\sqrt{1-x^2}}\)
\(\int_0^1\)\(\dfrac{2x^3-3x^2+x-4}{x^2+2x+1}dx\)
a\(\int_0^1\dfrac{dx}{x^4+4x^2+3}\)
b \(\int\dfrac{x^2-1}{x^4+1}\)
c\(\int\dfrac{dx}{x\left(x^3+1\right)}\)
d \(\int_0^1\dfrac{xdx}{x^4+x^2+1}\)
\(\int\dfrac{x^2-3}{x\left(x^4+3x^2+2\right)}dx\)
Anh Lâm ơi giúp em với, nên đặt gì làm ẩn bây giờ ạ?
\(\int_{-1}^0\)\(\dfrac{3x^2+3x+3}{x^3-3x+2}dx\)
\(\int_{-1}^0\) \(\dfrac{x^2-4x+4}{x^2-1}dx\)
\(\int_1^2\)\(\dfrac{x-4}{x\left(x+1\right)}dx\)
help me
tính
Câu 1: A=\(\int\dfrac{2SINX+COSX}{3SINX+2COSX}DX\)
Câu 2: \(I=\int\dfrac{X^3}{X^4+3X^2+2}\)
