Question

If `int1/(x + x^5)dx = f(x) + c`, then `intx^4/(x + x^5)dx` = ______

Options

• log x - f(x) + c

• f(x) + log x + c

• f(x) - log x + c

• `1/5x^5 f(x) + c`

Answer 1

If `int1/(x + x^5)dx = f(x) + c`, then `intx^4/(x + x^5)dx` = log x - f(x) + c

Explanation:

`intx^4/(x + x^5)dx = intx^4/(x(1 + x^4))dx`

= `int((1 + x^4) - 1)/(x(1 + x^4))dx`

= `int1/x dx - int1/(x + x^5)dx = logx - f(x) + c`