## Trending News

# 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

- 9 years agoFavorite 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