Question

Integrate 1/4+x^2

Answer 1

1/4 is a constant. x^2 gains a power of x.

(1/4)x + (1/3)x^3 + C

Answer 2

if it is
\[\int\frac{dx}{4+x^2}\] answer is
\[\frac{1}{2}\tan^{-1}(\frac{x}{2})\]

Answer 3

no method, just remember the derivative of arctangent and adjust appropriately. or look in the back of the book

Answer 4

where undoubtably is has a formula for
\[\int\frac{du}{a^2+u^2}\]

Answer 5

your teacher may want a trig sub, but it is rather silly since the derivative of
\[\tan^{-1}(x)\] is
\[\frac{1}{1+x^2}\]

Answer 6

what would u substitute for in this problem?

Answer 7

Wait, is the 4+x^2 all together under the 1?
If so, please use parentheses.

Use u-substitution for the arctan function.
a^2 = 4 u^2 = x^2
a = 2 u = x du = dx

\[\int\limits_{?}^{?} 1{/}(a ^{2} + u ^{2}) du = (1/a)\arctan(u/a) + C\]
So it turns out to be (1/2)*arctan(x/2) + C
The arctan is going to be the most common you will see on tests, since it has addition in the denominator. Remember to tell the difference between this, other trig integrals, natural logs, and negative powered terms.

Answer 8

ty very much:)