\(I=\int tan^2x\left(\dfrac{1}{cos^2x}-1\right)dx=\int tan^2x.\dfrac{1}{cos^2x}dx-\int tan^2xdx\)
\(=\int tan^2x.d\left(tanx\right)-\int\left(\dfrac{1}{cos^2x}-1\right)dx=\dfrac{1}{3}tan^3x-tanx+x+C\)
Bằng cách biến đổi các hàm số lượng giác, hãy tính :
a) \(\int\sin^4xdx\)
b) \(\int\dfrac{1}{\sin^3x}dx\)
c) \(\int\sin^3x\cos^4xdx\)
d) \(\int\sin^4x\cos^4xdx\)
e) \(\int\dfrac{1}{\cos x\sin^2x}dx\)
g) \(\int\dfrac{1+\sin x}{1+\cos x}dx\)
I=\(\int\limits^{\frac{\pi}{6}}_0\)\(\frac{tan^4xdx}{cos2x}\)
J=\(\int\limits^3_1\)\(\frac{3+lnx}{\left(x+1\right)^2}\)
K=\(\int\limits^1_0\)\(\frac{\left(2+xe^x\right)}{x^2+2x+1}\)dx
Tính nguyên hàm :
a) I= \(\int\dfrac{dx}{2sin^2x+5sinx.cosx+2cos^2x}\)
b) I= \(\int\dfrac{dx}{sin^2x+3sinx.cox+2cos^2x}\)
Tính nguyên hàm các hàm số sau:
1. \(I=\int\dfrac{cos^2x}{sin^8x}dx\)
2. \(I=\int\left(e^{sinx}+cosx\right)cosxdx\)
Tính \(I=\int x.\ln\left(x+1\right)dx\)
Tính nguyên hàm \(I=\int{\sqrt{2x-x^2}}dx\)
\(\int\dfrac{cotx}{sin^2x}dx\) = ?
A. \(-\dfrac{cot^2x}{2}+c\)
B. \(\dfrac{cot^2x}{2}+c\)
C. \(\dfrac{-tan^2x}{2}+c\)
D. \(\dfrac{tan^2x}{2}+c\)
\(\int\frac{tan^3x}{c\text{os}2x}dx\)
2) \(\int\frac{xe^x\left(4+4\left(s\text{inx}+c\text{os}x\right)+sin2x\right)}{\left(1+c\text{os}x\right)^2}\)
Tính tích phân :
\(I=\int\limits^1_0\frac{dx}{\left(x+1\right)^3}\)
