Question

$\int {\cos }^{-3/7}x{\sin }^{-11/7}xdx$ is equal to

• A. $\log |{\sin }^{4/7}x|+c$
• B. $\frac{4}{7}{\tan }^{4/7}x+c$
• C. $-\frac{7}{4}{\tan }^{-4/7}x+c$
• D. $\log |{\cos }^{3/7}x|+c$

Answer 1

The correct option is C $-\frac{7}{4}{\tan }^{-4/7}x+c$

$\int co{s}^{{}^{-3}{/}_7}xsi{n}^{{}^{-11}{/}_7}xdx=\int \frac{si{n}^{{}^3{/}_7}x}{si{n}^{{}^3{/}_7}x}co{s}^{{}^{-3}{/}_7}si{n}^{{}^{-11}{/}_7}dx$

$\int ta{n}^{{}^3{/}_7}xcose{c}^{2}xdx$

$-\int co{t}^{{}^{-3}{/}_7}xd\left(cotx\right)$

$-\frac{7}{4}co{t}^{{}^4{/}_7}x+c$

$\int co{s}^{{}^{-3}{/}_7}xsi{n}^{{}^{-11}{/}_7}xdx\cdot =-\frac{7}{4}ta{n}^{{}^{-4}{/}_7}x+c\cdot$