(Solved): Identify the form of each integral as being inverse sine, inverse tangent, logarithmic, or general ...

Identify the form of each integral as being inverse sine, inverse tangent, logarithmic, or general power. Do not integrate. In part (a), explain how the choice was made. (a) \( \int \frac{2 d x}{4+16 x^{2}} \) (b) \( \int \frac{2 d x}{4+16 x} \) (c) \( \int \frac{2 x d x}{\sqrt{4+16 x^{2}}} \) (a) Choose the correct form of the integral \( \int \frac{2 \mathrm{dx}}{4+16 \mathrm{x}^{2}} \) below and fill in the necessary boxes to complefe your answer. Logarithmic with the substitutions \( u=\quad \) and \( d u= \) Inverse tangent with the substitutions \( a=, u=, d u= \) Inverse sine with the substitutions \( a=, u=, d u= \) General power with the substitutions \( u=, d u=, n= \) (b) Choose the correct form of the integral \( \int \frac{2 d x}{4+16 x} \) below. General power Inverse sine Inverse tangent Logarithmic