undefined To solve an integral, we typically follow these steps: 1. **Understand the Integral**: Ensure clarity on what the integral is asking for and the limits of integration. 2. **Use Techniques**: Employ various integration techniques such as substitution, integration by parts, trigonometric identities, partial fractions, etc. 3. **Apply Rules**: Apply fundamental rules of integration, such as the power rule, the product rule, the chain rule, etc. 4. **Evaluate**: Once the integral is simplified, evaluate it by plugging in the limits of integration and computing the result.

Home > Calculus > Integrals of Trigonometric Functions

How do you solve this integral?

#inttan^2xdx#

Answer 1

Emma Aldridge

#int tan^2x dx = tanx -x +C#

Use the identity:

#tan^2x = sec^2x -1#

and remember that:

#d/(dx) tanx = sec^2x#

so we have:

#int tan^2x dx = int (sec^2x -1) dx = int sec^2xdx - int dx = tanx -x +C#

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Answer 2

William Abdalla

To solve an integral, we typically follow these steps:

Understand the Integral: Ensure clarity on what the integral is asking for and the limits of integration.
Use Techniques: Employ various integration techniques such as substitution, integration by parts, trigonometric identities, partial fractions, etc.
Apply Rules: Apply fundamental rules of integration, such as the power rule, the product rule, the chain rule, etc.
Evaluate: Once the integral is simplified, evaluate it by plugging in the limits of integration and computing the result.

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Answer from HIX Tutor

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.