Chapter 5: Q. 55 (page 465)

Solve the integral $\int \frac{3 + x}{\sqrt{9 - 4 x^{2}}} d x$

Short Answer

Expert verified

$- \frac{1}{4} \int \sqrt{(- 4 x^{2} + 9)} + \frac{3}{2} \sin^{- 1} (\frac{2 x}{3}) + c$

Step by step solution

Step 1. Given

$\int \frac{3 + x}{\sqrt{9 - 4 x^{2}}} d x$

Step 3. Calculation

$\int \frac{3 + x}{\sqrt{9 - 4 x^{2}}} d x = \int \frac{x}{\sqrt{9 - 4 x^{2}}} d x + \int \frac{3}{\sqrt{9 - 4 x^{2}}} d x = - \frac{1}{8} \int \frac{1}{\sqrt{u}} d x + \int \frac{3}{\sqrt{9 - 4 x^{2}}} d x [u = - 4 x^{2} + 9, d u = - 8 x d x] = - \frac{2 \sqrt{u}}{8} + \int \frac{3}{\sqrt{9 - 4 x^{2}}} d x = - \frac{\sqrt{u}}{4} + \int \frac{3}{\sqrt{9 - 4 x^{2}}} d x = - \frac{1}{4} \sqrt{(- 4 x^{2} + 9} + \int \frac{3}{\sqrt{9 - 4 x^{2}}} d x = - \frac{1}{4} \sqrt{(- 4 x^{2} + 9} + 3 \int \frac{1}{2} d u = - \frac{1}{4} \sqrt{(- 4 x^{2} + 9} + \frac{3}{2} (u) = - \frac{1}{4} \sqrt{(- 4 x^{2} + 9} + \frac{3}{2} (\sin^{- 1} (\frac{2 x}{3})) + C$

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Solve the integral $\int \frac{3 + x}{\sqrt{9 - 4 x^{2}}} d x$

Short Answer

Step by step solution

Step 1. Given

Step 3. Calculation

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Solve the integral∫3+x9-4x2dx

Short Answer

Step by step solution

Step 1. Given

Step 3. Calculation

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Most popular questions from this chapter

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Solve the integral $\int \frac{3 + x}{\sqrt{9 - 4 x^{2}}} d x$