Xét tính đúng sai của các khẳng định sau?
a) $\int{{{x}^{7}}dx=\dfrac{{{x}^{9}}}{9}+C}$
.b) $\int{\left( 5\sin x-9\cos x \right)dx=-5\cos x-9\sin x+C}$
c) $\int{\dfrac{1}{{{x}^{6}}}dx=-\dfrac{1}{7{{x}^{7}}}+C}$
d) $\int{\sqrt{x^{7}}}dx=\dfrac{2}{5}x^{\frac{5}{2}}+C$
Lời giải:
(Sai) $\int{{{x}^{7}}dx=\dfrac{{{x}^{9}}}{9}+C}$
(Đúng) $\int{\left( 5\sin x-9\cos x \right)dx=-5\cos x-9\sin x+C}$
(Sai) $\int{\dfrac{1}{{{x}^{6}}}dx=-\dfrac{1}{7{{x}^{7}}}+C}$
(Vì): $\int{\dfrac{1}{{{x}^{6}}}dx=-\dfrac{1}{5{{x}^{5}}}+C}$
(Sai) $\int{\sqrt{x^{7}}}dx=\dfrac{2}{5}x^{\frac{5}{2}}+C$
(Vì): $\int{\sqrt{x^{7}}}dx=\dfrac{2}{9}x^{\frac{9}{2}}+C$
(Sai) $\int{{{x}^{7}}dx=\dfrac{{{x}^{9}}}{9}+C}$
(Đúng) $\int{\left( 5\sin x-9\cos x \right)dx=-5\cos x-9\sin x+C}$
(Sai) $\int{\dfrac{1}{{{x}^{6}}}dx=-\dfrac{1}{7{{x}^{7}}}+C}$
(Sai) $\int{\sqrt{x^{7}}}dx=\dfrac{2}{5}x^{\frac{5}{2}}+C$