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original integral with dx = 9cosQ dQ . FORMATTING: Do not include dQ in your answer; it is already written for you. g) Next, use the work you've done and apply the substitution for x and dx. Then, use the right side of your cleverly-chosen trig identity to eliminate the square root, and simplify the integrand. This should transform the original integral, written in terms of x, into a new integral in terms of Q which does not contain any square roots! integral 1 / (x^2 sqrt(81 - x^2)) dx = integral g(Q) dQ The new integrand is g(Q) = . Q = theta FORMATTING: Your answer for g(Q) should not include any radicals (i.e. do not use sqrt()). It should not include absolute value (i.e. do not use abs()). It may be a mathematical expression involving trig functions and the variable Q. Pay attention to Mobius syntax for powers of trig functions, e.g. sin^2(a) must be written as (sin(a))^2. h) Now, integrate with respect to Q to obtain integral g(Q) dQ = +C. FORMATTING: Your answer should depend on the variable Q. Do not include the constant of integration in your answer; "(+C" is already written for you. i) Finally, rewrite your answer from h) in terms of the original variable x. Hint: Parts d) and/or e) may be useful. Final answer: integral 1 / (x^2 * sqrt(81 - x^2)) dx = +C. FORMATTING: Do not include the constant of integration in your answer; "+C" is already written for you.

          original integral with dx = 9*cosQ dQ .
FORMATTING: Do not include dQ in your answer; it is already written for you.
g) Next, use the work you've done and apply the substitution for x and dx. Then, use the right side of your cleverly-chosen trig identity to eliminate the square root, and simplify the integrand. This should transform the original integral, written in terms of x, into a new integral in terms of Q which does not contain any square roots!
integral 1 / (x^2 * sqrt(81 - x^2)) dx = integral g(Q) dQ
The new integrand is g(Q) = . Q = theta
FORMATTING: Your answer for g(Q) should not include any radicals (i.e. do not use sqrt()). It should not include absolute value (i.e. do not use abs()). It may be a mathematical expression involving trig functions and the variable Q. Pay attention to Mobius syntax for powers of trig functions, e.g. sin^2(a) must be written as (sin(a))^2.
h) Now, integrate with respect to Q to obtain integral g(Q) dQ = +C.
FORMATTING: Your answer should depend on the variable Q. Do not include the constant of integration in your answer; "(+C" is already written for you.
i) Finally, rewrite your answer from h) in terms of the original variable x.
Hint: Parts d) and/or e) may be useful.
Final answer: integral 1 / (x^2 * sqrt(81 - x^2)) dx = +C.
FORMATTING: Do not include the constant of integration in your answer; "+C" is already written for you.

original integral with dx = 9*cosQ dQ .
FORMATTING: Do not include dQ in your answer; it is already written for you.
g) Next, use the work you've done and apply the substitution for x and dx. Then, use the right side of your cleverly-chosen trig identity to eliminate the square root, and simplify the integrand. This should transform the original integral, written in terms of x, into a new integral in terms of Q which does not contain any square roots!
integral 1 / (x^2 * sqrt(81 - x^2)) dx = integral g(Q) dQ
The new integrand is g(Q) = . Q = theta
FORMATTING: Your answer for g(Q) should not include any radicals (i.e. do not use sqrt()). It should not include absolute value (i.e. do not use abs()). It may be a mathematical expression involving trig functions and the variable Q. Pay attention to Mobius syntax for powers of trig functions, e.g. sin^2(a) must be written as (sin(a))^2.
h) Now, integrate with respect to Q to obtain integral g(Q) dQ = +C.
FORMATTING: Your answer should depend on the variable Q. Do not include the constant of integration in your answer; "(+C" is already written for you.
i) Finally, rewrite your answer from h) in terms of the original variable x.
Hint: Parts d) and/or e) may be useful.
Final answer: integral 1 / (x^2 * sqrt(81 - x^2)) dx = +C.
FORMATTING: Do not include the constant of integration in your answer; "+C" is already written for you.

Added by Vitelma T.

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