Help with maths questions?

(a) Given that y = tan^-1x , show that

dy/dx = 1/(x^2 + 1)

(b) Differentiate ln(x^2 + 1) with respect to x.

(c) Use the results derived from (a) and (b) to find the integral of:

(3 + x)/(1 + x^2) dx

Please show workings.

1 Answer

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  • 9 years ago
    Favorite Answer

    Simplifying

    (3 + x) = (1 + x2) * dx

    Remove parenthesis around (3 + x)

    3 + x = (1 + x2) * dx

    Reorder the terms for easier multiplication:

    3 + x = dx(1 + x2)

    3 + x = (1 * dx + x2 * dx)

    3 + x = (1dx + dx3)

    Solving

    3 + x = 1dx + dx3

    Solving for variable 'x'.

    Reorder the terms:

    3 + -1dx + -1dx3 + x = 1dx + dx3 + -1dx + -1dx3

    Reorder the terms:

    3 + -1dx + -1dx3 + x = 1dx + -1dx + dx3 + -1dx3

    Combine like terms: 1dx + -1dx = 0

    3 + -1dx + -1dx3 + x = 0 + dx3 + -1dx3

    3 + -1dx + -1dx3 + x = dx3 + -1dx3

    Combine like terms: dx3 + -1dx3 = 0

    3 + -1dx + -1dx3 + x = 0

    The solution to this equation could not be determined.

    Source(s): Algebra
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