Choose the correct answerThe Value of `int_(-pi/2)^(pi/2)(x^3+xcosx+tan^5x+1)dx`is(A) 0 (B) 2 (C) `pi` (D) 1

Explanation

To solve the integral \( I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^3 + x \cos x + \tan^5 x + 1) \, dx \), we can break it down into parts and analyze the properties of the functions involved.

### Step 1: Split the Integral
We can express the integral as:
\[ I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} x^3 \, dx + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} x \cos x \, dx + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \tan^5 x \, dx + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 1 \, dx \]

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