dx=t(1+t^2)sec^2xdt

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Solution for dx=t(1+t^2)sec^2xdt equation: 


Simplifying
dx = t(1 + t2) * sec2xdt

Reorder the terms for easier multiplication:
dx = t * c2destx(1 + t2)

Multiply t * c2destx
dx = c2dest2x(1 + t2)
dx = (1 * c2dest2x + t2 * c2dest2x)
dx = (1c2dest2x + c2dest4x)

Solving
dx = 1c2dest2x + c2dest4x

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-1c2dest2x' to each side of the equation.
-1c2dest2x + dx = 1c2dest2x + -1c2dest2x + c2dest4x

Combine like terms: 1c2dest2x + -1c2dest2x = 0
-1c2dest2x + dx = 0 + c2dest4x
-1c2dest2x + dx = c2dest4x

Add '-1c2dest4x' to each side of the equation.
-1c2dest2x + -1c2dest4x + dx = c2dest4x + -1c2dest4x

Combine like terms: c2dest4x + -1c2dest4x = 0
-1c2dest2x + -1c2dest4x + dx = 0

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(-1c2est2 + -1c2est4 + 1) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
dx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1c2est2 + -1c2est4 + 1)' equal to zero and attempt to solve:

Simplifying
-1c2est2 + -1c2est4 + 1 = 0

Reorder the terms:
1 + -1c2est2 + -1c2est4 = 0

Solving
1 + -1c2est2 + -1c2est4 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1c2est2 + -1 + -1c2est4 = 0 + -1

Reorder the terms:
1 + -1 + -1c2est2 + -1c2est4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1c2est2 + -1c2est4 = 0 + -1
-1c2est2 + -1c2est4 = 0 + -1

Combine like terms: 0 + -1 = -1
-1c2est2 + -1c2est4 = -1

Add 'c2est2' to each side of the equation.
-1c2est2 + c2est2 + -1c2est4 = -1 + c2est2

Combine like terms: -1c2est2 + c2est2 = 0
0 + -1c2est4 = -1 + c2est2
-1c2est4 = -1 + c2est2

Add 'c2est4' to each side of the equation.
-1c2est4 + c2est4 = -1 + c2est2 + c2est4

Combine like terms: -1c2est4 + c2est4 = 0
0 = -1 + c2est2 + c2est4

Simplifying
0 = -1 + c2est2 + c2est4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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