Enter a problem...
Calculus Examples
Step 1
Step 1.1
Multiply both sides by .
Step 1.2
Cancel the common factor of .
Step 1.2.1
Cancel the common factor.
Step 1.2.2
Rewrite the expression.
Step 1.3
Rewrite the equation.
Step 2
Step 2.1
Set up an integral on each side.
Step 2.2
Integrate the left side.
Step 2.2.1
Let . Then , so . Rewrite using and .
Step 2.2.1.1
Let . Find .
Step 2.2.1.1.1
Rewrite.
Step 2.2.1.1.2
Divide by .
Step 2.2.1.2
Rewrite the problem using and .
Step 2.2.2
Move the negative in front of the fraction.
Step 2.2.3
Since is constant with respect to , move out of the integral.
Step 2.2.4
Apply basic rules of exponents.
Step 2.2.4.1
Move out of the denominator by raising it to the power.
Step 2.2.4.2
Multiply the exponents in .
Step 2.2.4.2.1
Apply the power rule and multiply exponents, .
Step 2.2.4.2.2
Multiply by .
Step 2.2.5
By the Power Rule, the integral of with respect to is .
Step 2.2.6
Simplify.
Step 2.2.6.1
Rewrite as .
Step 2.2.6.2
Simplify.
Step 2.2.6.2.1
Multiply by .
Step 2.2.6.2.2
Multiply by .
Step 2.2.7
Replace all occurrences of with .
Step 2.3
Apply the constant rule.
Step 2.4
Group the constant of integration on the right side as .
Step 3
Step 3.1
Find the LCD of the terms in the equation.
Step 3.1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.1.2
Remove parentheses.
Step 3.1.3
The LCM of one and any expression is the expression.
Step 3.2
Multiply each term in by to eliminate the fractions.
Step 3.2.1
Multiply each term in by .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of .
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Rewrite the expression.
Step 3.2.3
Simplify the right side.
Step 3.2.3.1
Simplify each term.
Step 3.2.3.1.1
Apply the distributive property.
Step 3.2.3.1.2
Multiply by .
Step 3.2.3.1.3
Rewrite using the commutative property of multiplication.
Step 3.2.3.1.4
Apply the distributive property.
Step 3.2.3.1.5
Multiply by .
Step 3.2.3.1.6
Rewrite using the commutative property of multiplication.
Step 3.3
Solve the equation.
Step 3.3.1
Rewrite the equation as .
Step 3.3.2
Move all terms not containing to the right side of the equation.
Step 3.3.2.1
Subtract from both sides of the equation.
Step 3.3.2.2
Subtract from both sides of the equation.
Step 3.3.3
Factor out of .
Step 3.3.3.1
Factor out of .
Step 3.3.3.2
Factor out of .
Step 3.3.3.3
Factor out of .
Step 3.3.4
Divide each term in by and simplify.
Step 3.3.4.1
Divide each term in by .
Step 3.3.4.2
Simplify the left side.
Step 3.3.4.2.1
Cancel the common factor of .
Step 3.3.4.2.1.1
Cancel the common factor.
Step 3.3.4.2.1.2
Divide by .
Step 3.3.4.3
Simplify the right side.
Step 3.3.4.3.1
Simplify each term.
Step 3.3.4.3.1.1
Move the negative in front of the fraction.
Step 3.3.4.3.1.2
Move the negative in front of the fraction.
Step 3.3.4.3.2
Simplify terms.
Step 3.3.4.3.2.1
Combine the numerators over the common denominator.
Step 3.3.4.3.2.2
Combine the numerators over the common denominator.
Step 3.3.4.3.2.3
Factor out of .
Step 3.3.4.3.2.4
Factor out of .
Step 3.3.4.3.2.5
Rewrite negatives.
Step 3.3.4.3.2.5.1
Rewrite as .
Step 3.3.4.3.2.5.2
Move the negative in front of the fraction.
Step 4
Simplify the constant of integration.