Enter a problem...
Calculus Examples
Step 1
Step 1.1
Divide each term in by and simplify.
Step 1.1.1
Divide each term in by .
Step 1.1.2
Simplify the left side.
Step 1.1.2.1
Cancel the common factor of .
Step 1.1.2.1.1
Cancel the common factor.
Step 1.1.2.1.2
Divide by .
Step 1.1.3
Simplify the right side.
Step 1.1.3.1
Simplify each term.
Step 1.1.3.1.1
Cancel the common factor of and .
Step 1.1.3.1.1.1
Factor out of .
Step 1.1.3.1.1.2
Cancel the common factors.
Step 1.1.3.1.1.2.1
Factor out of .
Step 1.1.3.1.1.2.2
Cancel the common factor.
Step 1.1.3.1.1.2.3
Rewrite the expression.
Step 1.1.3.1.2
Cancel the common factor of .
Step 1.1.3.1.2.1
Cancel the common factor.
Step 1.1.3.1.2.2
Rewrite the expression.
Step 1.2
Rewrite as .
Step 2
Let . Substitute for .
Step 3
Solve for .
Step 4
Use the product rule to find the derivative of with respect to .
Step 5
Substitute for .
Step 6
Step 6.1
Separate the variables.
Step 6.1.1
Solve for .
Step 6.1.1.1
Move all terms not containing to the right side of the equation.
Step 6.1.1.1.1
Subtract from both sides of the equation.
Step 6.1.1.1.2
Combine the opposite terms in .
Step 6.1.1.1.2.1
Subtract from .
Step 6.1.1.1.2.2
Add and .
Step 6.1.1.2
Divide each term in by and simplify.
Step 6.1.1.2.1
Divide each term in by .
Step 6.1.1.2.2
Simplify the left side.
Step 6.1.1.2.2.1
Cancel the common factor of .
Step 6.1.1.2.2.1.1
Cancel the common factor.
Step 6.1.1.2.2.1.2
Divide by .
Step 6.1.2
Combine the numerators over the common denominator.
Step 6.1.3
Multiply both sides by .
Step 6.1.4
Cancel the common factor of .
Step 6.1.4.1
Cancel the common factor.
Step 6.1.4.2
Rewrite the expression.
Step 6.1.5
Rewrite the equation.
Step 6.2
Integrate both sides.
Step 6.2.1
Set up an integral on each side.
Step 6.2.2
Integrate the left side.
Step 6.2.2.1
Rewrite as .
Step 6.2.2.2
The integral of with respect to is .
Step 6.2.3
The integral of with respect to is .
Step 6.2.4
Group the constant of integration on the right side as .
Step 6.3
Take the inverse arctangent of both sides of the equation to extract from inside the arctangent.
Step 7
Substitute for .
Step 8
Step 8.1
Multiply both sides by .
Step 8.2
Simplify.
Step 8.2.1
Simplify the left side.
Step 8.2.1.1
Cancel the common factor of .
Step 8.2.1.1.1
Cancel the common factor.
Step 8.2.1.1.2
Rewrite the expression.
Step 8.2.2
Simplify the right side.
Step 8.2.2.1
Reorder factors in .