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Q: What is the integral of 1 divided by the cosine of x with respect to x?

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I will assume that this is sopposed to be integrated with respect to x. To make this problem easier, imagine that the integrand is x raised to the negative 3. The integral is 1/(-2x-2) plus some constant c.

Secant is 1 over cosine and cosine 0 equals 1.

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A cosine of a triangle is the length of the leg adjacent to a specific angle divided by the hypotenuse. Another way of putting it is that a cosine of an angle is x/r, or the x-coordinate of the endpoint divided by the distance of the endpoint from the origin. In trigonometry, if this angle were to be zero radians or zero degrees, the triangle would become a short, flat line pointing directly to the right. In that case, the distance of the endpoint from the origin and the x-value of this point are one and the same. Thus, the ratio between them is 1, and the cosine of zero is 1. Also, the power series for cosine is as follows (where the angle is in radians): cos(x) = 1 - x^2/2 + x^4/24 - x^6/720 - x^8/40320 + ... (The denominators are the factorials of even numbers.) If you put x=0, you get cos(0)=1.

The integral of -x2 is -1/3 x3 .

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âˆ« 1/cos2(x) dx = tan(x) + C C is the constant of integration.

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The integral of cosine cubed is sinx- 1/3 sin cubed x + c

if you are integrating with respect to x, the indefinite integral of 1 is just x

âˆ« (1/x) dx = ln(x) + C C is the constant of integration.

âˆ« 1/sinh2(x) dx = -cotanh + C C is the constant of integration.

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I will assume that this is sopposed to be integrated with respect to x. To make this problem easier, imagine that the integrand is x raised to the negative 3. The integral is 1/(-2x-2) plus some constant c.

Ã¢Ë†Â« 1/sin2(x) dx = -cot(x) + CC is the constant of integration.

âˆ« 1/sin(x) dx = ln(tan(x/2)) + C C is the constant of integration.

There can be no definite integral because the limits of integration are not specified. The indefinite integral of 1/x2 is -1/x + C

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