Calculus Examples

Evaluate the Integral integral of (2x^2+7x-3)/(x-2) with respect to x
Step 1
Divide by .
Tap for more steps...
Step 1.1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
-+-
Step 1.2
Divide the highest order term in the dividend by the highest order term in divisor .
-+-
Step 1.3
Multiply the new quotient term by the divisor.
-+-
+-
Step 1.4
The expression needs to be subtracted from the dividend, so change all the signs in
-+-
-+
Step 1.5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-+-
-+
+
Step 1.6
Pull the next terms from the original dividend down into the current dividend.
-+-
-+
+-
Step 1.7
Divide the highest order term in the dividend by the highest order term in divisor .
+
-+-
-+
+-
Step 1.8
Multiply the new quotient term by the divisor.
+
-+-
-+
+-
+-
Step 1.9
The expression needs to be subtracted from the dividend, so change all the signs in
+
-+-
-+
+-
-+
Step 1.10
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+
-+-
-+
+-
-+
+
Step 1.11
The final answer is the quotient plus the remainder over the divisor.
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Apply the constant rule.
Step 6
Combine and .
Step 7
Since is constant with respect to , move out of the integral.
Step 8
Let . Then . Rewrite using and .
Tap for more steps...
Step 8.1
Let . Find .
Tap for more steps...
Step 8.1.1
Differentiate .
Step 8.1.2
By the Sum Rule, the derivative of with respect to is .
Step 8.1.3
Differentiate using the Power Rule which states that is where .
Step 8.1.4
Since is constant with respect to , the derivative of with respect to is .
Step 8.1.5
Add and .
Step 8.2
Rewrite the problem using and .
Step 9
The integral of with respect to is .
Step 10
Simplify.
Step 11
Replace all occurrences of with .