# What is the Integral of # (1+tanx)^5 * (sec^2(x)) dx #?

The answer is

We do this integral by substitution

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To integrate the given expression ( \int (1 + \tan(x))^5 \cdot \sec^2(x) , dx ), use the substitution method. Let ( u = 1 + \tan(x) ), then ( du = \sec^2(x) , dx ). Substituting these into the integral, you get ( \int u^5 , du ). Now integrate ( u^5 ) with respect to ( u ) to get ( \frac{u^6}{6} + C ), where ( C ) is the constant of integration. Finally, substitute back ( u = 1 + \tan(x) ) to get the final result ( \frac{(1 + \tan(x))^6}{6} + C ).

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The integral of (1 + tan(x))^5 * (sec^2(x)) dx equals (1/6) * (1 + tan(x))^6 + C, where C is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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