Solve this integral: ∫ 1 16 + x 2 d x

Question

Solve this integral:  ∫      1          16      +              x                  2                      d  x

mangoslush27fig · Accepted Answer

Since the denominator fits the form       a          2        +      x          2      , let&#039;s use Rule #  2 from the section above. We let   x  =  a  tan  ⁡  u, and   d  x  =  4      sec          2        ⁡  u.Substituting the variables from the above, we have:  ∫      1          16      +      (      4      tan      ⁡      u              )                  2                      ×  4      sec          2        ⁡  u  d  uAfter simplifying, we have:  ∫      1    4    d  uBy the Power Rule, the integral is:      u    4  From the earlier steps, we know that   x  =  a  tan  ⁡  u, and solving for   u we have:  u  =      tan          −      1        ⁡  (      1    4    x  )The only step remaining is to substitute the value of   u back into the earlier integral, namely       u    4  . After the substitution, we have:                    tan                  −          1                    ⁡      (              1        4            )      x        4    +  C

Solve this integral: int 1/(16+x^2) dx

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