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Study Resources (Calculus)

For each problem below, solve the I.V.P or differential equation using only these three methods: solving separable differential equation, solving linear differential equations, or solving exact differential equations. If an equation is not solvable using these techniques show and explain why it cannot be solved with these techniques. (only one.
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For each of the following use the comparison test for improper integrals to determine whether the integral is convergent or divergent: 1. \(\int_{1}^{inf}(1/(7\sqrt{x}+4e^{3x}))dx\) 2. \(\int_{1}^{inf}(x^{4}/(4x^{6}+5))dx\) 3. \(\int_{1}^{inf}(x^{4}/(8x^{6}-1))dx\) 4. \(\int_{1}^{inf}(x^{6}/(9x^{6}-1))dx\) 5. \(\int_{1}^{inf}(x^{5}/(7x^{5}+1))dx\)  .
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