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Integrate the function $\frac{7}{\left(x-9\right)\left(x^2+4\right)}$ from $- \infty $ to $7$

Step-by-step Solution

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Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

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Rewrite the fraction $\frac{7}{\left(x-9\right)\left(x^2+4\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{7}{\left(x-9\right)\left(x^2+4\right)}=\frac{A}{x-9}+\frac{Bx+C}{x^2+4}$

Learn how to solve simplification of algebraic expressions problems step by step online.

$\frac{7}{\left(x-9\right)\left(x^2+4\right)}=\frac{A}{x-9}+\frac{Bx+C}{x^2+4}$

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Learn how to solve simplification of algebraic expressions problems step by step online. Integrate the function 7/((x-9)(x^2+4)) from -infinity to 7. Rewrite the fraction \frac{7}{\left(x-9\right)\left(x^2+4\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x-9\right)\left(x^2+4\right). Multiplying polynomials. Simplifying.

Final answer to the problem

The integral diverges.

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (7/(x-9)(x^2+4))dx from -1infinity to 7 using basic integralsSolve integral of (7/(x-9)(x^2+4))dx from -1infinity to 7 using u-substitutionSolve integral of (7/(x-9)(x^2+4))dx from -1infinity to 7 using integration by partsSolve integral of (7/(x-9)(x^2+4))dx from -1infinity to 7 using trigonometric substitution

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Function Plot

Plotting: $\frac{7}{\left(x-9\right)\left(x^2+4\right)}$

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Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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