The value of $\int\left(3 x^2 \tan \frac

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

The value of $\int\left(3 x^2 \tan \frac{1}{x}-x \sec ^2 \frac{1}{x}\right) d x$ , is

Options:

$x^3 \tan \frac{1}{x}+C$

$x^2 \tan \frac{1}{x}+C$

$x \tan \frac{1}{x}+c$

none of these

Correct Answer:

$x^3 \tan \frac{1}{x}+C$

Explanation:

Let

$I=\int\left(3 x^2 \tan \frac{1}{x}-x \sec ^2 \frac{1}{x}\right) d x$

$\Rightarrow I =\int 3 x^2 \tan \frac{1}{x} d x-\int x \sec ^2 \frac{1}{x} d x$

$\Rightarrow I =x^3 \tan \frac{1}{x}+\int x \sec ^2 \frac{1}{x} d x-\int x \sec ^2 \frac{1}{x} d x+C$

$=x^3 \tan \frac{1}{x}+C$