JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int {{{\sec }^{2/3}}\,x\,\cos e{c^{4/3}}} x\,dx\) is equal to : (Here \(C\) is a constant of integration)
- A \(3\,{\tan ^{ - 1/3}}\,x + C\)
- B \( - \frac{3}{4}{\tan ^{ - 4/3}}\,x + C\)
- C \(-3\,{\cot ^{ - 1/3}}\,x + C\)
- D \(-3\,{\tan ^{ - 1/3}}\,x + C\)
Answer & Solution
Correct Answer
(D) \(-3\,{\tan ^{ - 1/3}}\,x + C\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \frac{\mathrm{dx}}{(\sin x)^{4 / 3} \cdot(\cos x)^{2 / 3}}\) \(I=\int \frac{d x}{\left(\frac{\sin x}{\cos x}\right)^{4 / 3} \cdot \cos ^{2} x}\) \(\Rightarrow \mathrm{I}=\int \frac{\sec ^{2} x}{(\tan x)^{4 / 3}} d x\) \(\text { put } \tan x=t\)…
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