Toán Lớp 12: 21) tính nguyên hàm
$\int$cos4x.sinx dx
22) tính nguyên hàm
$\int$cos3x.cos2x dx
23) tính nguyên hàm
$\int$sin5x.sin2x dx
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Toán Lớp 12: 21) tính nguyên hàm
$\int$cos4x.sinx dx
22) tính nguyên hàm
$\int$cos3x.cos2x dx
23) tính nguyên hàm
$\int$sin5x.sin2x dx
Comments ( 2 )
21)\quad \displaystyle\int\cos4x.\sin xdx
= \dfrac16\cos3x – \dfrac{1}{10}\cos5x + C\\
22)\quad \displaystyle\int\cos3x\cos2xdx
= \dfrac{1}{10}\sin5x + \dfrac12\sin x + C\\
23)\quad \displaystyle\int\sin5x.\sin2xdx
= \dfrac{1}{6}\sin3x – \dfrac{1}{14}\sin7x + C
\end{array}\)
21)\quad \displaystyle\int\cos4x.\sin xdx\\
= \dfrac12\displaystyle\int(\sin5x – \sin3x)dx\\
= \dfrac12\left(-\dfrac15\cos5x + \dfrac13\cos3x + C\right)\\
= \dfrac16\cos3x – \dfrac{1}{10}\cos5x + C\\
22)\quad \displaystyle\int\cos3x\cos2xdx\\
= \dfrac12\displaystyle\int(\cos5x + \cos x)dx\\
= \dfrac12\left(\dfrac15\sin5x + \sin x + C\right)dx\\
= \dfrac{1}{10}\sin5x + \dfrac12\sin x + C\\
23)\quad \displaystyle\int\sin5x.\sin2xdx\\
= \dfrac12\displaystyle\int(\cos3x – \cos7x)dx\\
= \dfrac12\left(\dfrac13\sin3x – \dfrac17\sin7x + C\right)\\
= \dfrac{1}{6}\sin3x – \dfrac{1}{14}\sin7x + C
\end{array}\)