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What you the integral of 1?
if you are integrating with respect to x, the indefinite integral of 1 is just x
What is the integral of 3 over 3x?
The 3s would cancel and it would become the integral of 1/x which is ln x.
What is the integral of 1 divided by 2x squared?
0.5
What is the integral of tan squared x cosine to the 5th power x dx?
Since you did not specify any limits of integration, I assume you are looking for the indefinite integral of this expression: tan2(x)cos5(x) with respect to x (dx). Using the following identity: tan(x) = sin(x) / cos(x) The original expression can be rewritten as: (sin2(x) / cos2(x))cos5(x) Which further simplifies to: sin2(x)cos3(x) Which can be expanded to: sin2(x)cos2(x)cos(x) Using the identity: sin2(x) + cos2(x) = 1 which implies: cos2(x) = 1 - sin2(x) which makes the expression from above able to be simplified into: sin2(x)(1 - sin2(x))cos(x) From here, you can use u-substitution by using the substitution: u = sin(x) du = cos(x) dx => dx = du/cos(x) So after u substitution: int(sin2(x)(1 - sin2(x))cos(x)) dx becomes: int(u2(1-u2)) du int(u2-u4) du From here, elementary antiderivatives can be used: anti(u2) = (1/3)(u3) anti(u4) = (1/5)(u5) which yields a final indefinite integral in u of: (1/3)u3-(1/5)u5 + C where C is the constant of integration (since this is an indefinite integral). Back-substituting with the u-substitution from before (u=sin(x)), the final indefinite integral in x is: (1/3)sin3(x) - (1/5)sin5(x) + C
What is the antiderivative of x to the 1?
By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
