How do you integrate #(x^3+4)/(x^2+4)# using partial fractions?
to first perform long division. Instead, we proceed as under :
Enjoy maths.!
By signing up, you agree to our Terms of Service and Privacy Policy
To integrate ( \frac{x^3+4}{x^2+4} ) using partial fractions, follow these steps:

First, factor the denominator (x^2 + 4) as ( (x + 2i)(x  2i) ).

Since the denominator does not have any real roots, we will have complex conjugate roots. So, we can express the fraction as:
[ \frac{x^3+4}{x^2+4} = \frac{Ax + B}{x^2+4} + \frac{Cx + D}{(x^2+4)^2} ]

Multiply both sides by ( x^2 + 4 ) to clear the denominators.

Equate coefficients of like terms on both sides.

Solve the resulting system of equations to find the values of ( A ), ( B ), ( C ), and ( D ).

Once you find ( A ), ( B ), ( C ), and ( D ), integrate each term separately.

Finally, sum up the integrals obtained from each term to get the final result.
This process allows you to integrate the given expression using partial fractions.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you integrate #int x^2 /sqrt( 16+x^4 )dx# using trigonometric substitution?
 How do you integrate #int (3x)/((x^2+3)(x+3)) dx# using partial fractions?
 How do you integrate #int x^3sqrt(1+x^2)# using integration by parts?
 How do you integrate #inte^(1/x)/x^2# using substitution?
 How do you find the antiderivative of #int (xsinxcosx) dx#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7