Integration U-substitution - Trigonometric Practice Problems Online

Evaluate the integral \(\displaystyle{ \int { \frac{10x}{\sqrt{3-2x-x^2}} dx }} ,\) using \(C\) as the constant of integration.

\[ -10 \sqrt{3-2x-x^2} - 10 \cos^{-1} \left( \frac{x+1}{2} \right) + C \] \[ -10 \sqrt{3-2x-x^2} - 10 \sin^{-1} \left( \frac{x+3}{2} \right) + C \] \[ -10 \sqrt{3-2x-x^2} - 10 \tan^{-1} \left( \frac{x}{2} \right) + C \] \[ -10 \sqrt{3-2x-x^2} - 10 \sin^{-1} \left( \frac{x+1}{2} \right) + C \]

Evaluate the integral \(\displaystyle{ \int { \frac { 47 \sqrt{9-x^2} }{x^2 } dx } },\) using \(C\) as the constant of integration.

\[ -\frac{ 47 \sqrt{ 9-x^2 } }{x} - 47\cot^{-1} \left( \frac{x}{3} \right) + C \] \[ -\frac{ 47 \sqrt{ 9-x^2 } }{x} - 47\sin^{-1} \left( \frac{x}{3} \right) + C \] \[ -\frac{ 47 \sqrt{ 9-x^2 } }{x} - 47\tan^{-1} \left( \frac{x}{3} \right) + C \] \[ -\frac{ 47 \sqrt{ 9-x^2 } }{x} - 47\cos^{-1} \left( \frac{x}{3} \right) + C \]

Evaluate the integral \(\displaystyle{ \int{\frac{15}{x^2\sqrt{x^2+4}}dx}},\) using \(C\) as the constant of integration.

Evaluate the integral \(\displaystyle{ 43\int { \cos^3 x dx} },\) using \(C\) as the constant of integration.

Given \( a>0 ,\) evaluate the integral \( \displaystyle{ 41 \int { \frac{dx}{\sqrt{x^2 - a^2}} }}, \) using \(C\) as the constant of integration.

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Integration U-substitution - Trigonometric

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