fertilizeki

2022-01-01

Trigonometric integrals Evaluate the following integrals.

$\int {\mathrm{tan}}^{2}xdx$

zesponderyd

Beginner2022-01-02Added 41 answers

Step 1

Explanation:

Given that,

$\int {\mathrm{tan}}^{2}xdx$

We know that,

${\mathrm{tan}}^{2}x={\mathrm{sec}}^{2}x-1$

Now integrate

$\int {\mathrm{tan}}^{2}xdx=\int {\mathrm{sec}}^{2}x-1dx$

$\int {\mathrm{tan}}^{2}xdx=\int {\mathrm{sec}}^{2}xdx-\int 1dx$

$\int {\mathrm{tan}}^{2}xdx=\mathrm{tan}x-x+C$

Step 2

Hence,

The integral of$\int {\mathrm{tan}}^{2}xdx$ is $\mathrm{tan}x-x+C$ where C is integral constant.

Explanation:

Given that,

We know that,

Now integrate

Step 2

Hence,

The integral of

Jim Hunt

Beginner2022-01-03Added 45 answers

Expand the expression

Evaluate

Add C

Final Answer:

Vasquez

Expert2022-01-07Added 669 answers

We make a trigonometric substitution:

Simplify the expression: The

degree of the numerator P(x) is greater than or equal to the degree of the denominator Q(x), so we divide the polynomials.

Integrating the integer part, we get:

Integrating further, we get:

Answer:

Returning to the change of variables

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