MCQ
$\int \cos ^{-\frac{3}{7}} x \cdot \sin ^{-\frac{11}{7}} x \cdot d x=$
- A$\log \left(\sin ^{-\frac{4}{7}} x\right)+c$
- B$\frac{4}{7} \tan ^{\frac{4}{7}} x+c$
- ✓$-\frac{7}{4} \tan ^{-\frac{4}{7}} x+c$
- D$\log \left(\cos ^{\frac{3}{7}} x\right)+c$
✓
Answer
Correct option: C.
$-\frac{7}{4} \tan ^{-\frac{4}{7}} x+c$
$-\frac{7}{4} \tan ^{-\frac{4}{7}} x+c$
Hint:
$\int \cos ^{-\frac{3}{7}} x \sin ^{-\frac{11}{7}} x d x$
$=\int \frac{\sin ^{-\frac{11}{7}} x}{\cos ^{-\frac{11}{7}} x-\cos ^2 x} d x $
$ =\int \tan ^{-\frac{111}{7}} x \sec ^2 x d x$
Put $tan x = t.$
Hint:
$\int \cos ^{-\frac{3}{7}} x \sin ^{-\frac{11}{7}} x d x$
$=\int \frac{\sin ^{-\frac{11}{7}} x}{\cos ^{-\frac{11}{7}} x-\cos ^2 x} d x $
$ =\int \tan ^{-\frac{111}{7}} x \sec ^2 x d x$
Put $tan x = t.$
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