MCQ
$\int {{{\sec }^{2/3}}\,x\,\cos e{c^{4/3}}} x\,dx$ મેળવો.
- A$3\,{\tan ^{ - 1/3}}\,x + C$
- B$ - \frac{3}{4}{\tan ^{ - 4/3}}\,x + C$
- C$-3\,{\cot ^{ - 1/3}}\,x + C$
- ✓$-3\,{\tan ^{ - 1/3}}\,x + C$
$I=\int \frac{d x}{\left(\frac{\sin x}{\cos x}\right)^{4 / 3} \cdot \cos ^{2} x}$
$\Rightarrow \mathrm{I}=\int \frac{\sec ^{2} x}{(\tan x)^{4 / 3}} d x$
$\text { put } \tan x=t$
$ \Rightarrow \sec ^{2} x d x=d t$
$\therefore \mathrm{I}=\int \frac{\mathrm{dt}}{\mathrm{t}^{4 / 3}}$
$ \Rightarrow \mathrm{I}=\frac{-3}{\mathrm{t}^{1 / 3}}+\mathrm{c}$
$\Rightarrow \mathrm{I}=\frac{-3}{(\tan \mathrm{x})^{1 / 3}}+\mathrm{c}$
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