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Integration Techniques

Writing an integral down is only the first step. A toolkit of techniques can help find its value, from substitutions to trigonometry to partial fractions to differentiation.

Trigonometric Substitution

         

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

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

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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