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7-1.Indefinite Integral question bank (Mathematics)

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Q1.

$\int \left(\frac{x-3}{x^2+9}\right)^2 \, dx =$

(A)

$\frac{1}{3} \tan^{-1}\left(\frac{x}{3}\right) - \frac{3}{x^2+9} + c$,where $c$ is the constant of integration.

(B)

$\frac{1}{3} \tan^{-1}\left(\frac{x}{3}\right) - \frac{1}{x^2+9} + c$,where $c$ is the constant of integration.

(C)

$\frac{1}{3} \tan^{-1}\left(\frac{x}{3}\right) + \frac{3}{x^2+9} + c$,where $c$ is the constant of integration.

(D)

$\frac{1}{3} \tan^{-1}\left(\frac{x}{3}\right) + \frac{1}{x^2+9} + c$,where $c$ is the constant of integration.

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Q2.

$\int \sqrt{x^2+3x} \, dx =$

(A)

$\sqrt{x^2+3x} + \log \sqrt{x^2+3x} + c$

(B)

$\frac{2x+3}{4} \sqrt{x^2+3x} - \frac{9}{8} \log \left| x + \frac{3}{2} + \sqrt{x^2+3x} \right| + c$

(C)

$x \sqrt{x^2+3x} + \log \left| x + \sqrt{x^2+3x} \right| + c$

(D)

$x + 3 \sqrt{x^2+3x} + \frac{3}{2} \log \left| x + \sqrt{x^2+3x} \right| + c$

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