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Question

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


A
log|sin4/7x|+c
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B
47tan4/7x+c
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C
74tan4/7x+c
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D
log|cos3/7x|+c
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Solution

The correct option is C $$ -\displaystyle \frac{7}{4}\tan^{-4/7}x+c$$
$$\int  cos ^{^{-3}/_{7}} xsin ^{^{-11}/_{7}}x dx =\int  \dfrac{sin ^{^{3}/_{7}}x}{sin ^{^{3}/_{7}}x} cos ^{^{-3}/_{7}}  sin ^{^{-11}/_{7}}  dx$$
$$\int  tan ^{^{3}/_{7}}x  cosec ^{2}x   dx$$
$$-\int  cot^{^{-3}/_{7}}x  d (cot   x)$$
$$-\dfrac{7}{4}  cot  ^{^{4}/_{7}}x+c$$
$$\int  cos^{^{-3}/_{7}}x  sin^{^{-11}/_{7}}x  dx \cdot  =-\dfrac{7}{4}  tan ^{^{-4}/_{7}}x+c\cdot$$

Mathematics

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