sqrt 5 x x 2 dx

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The Integral Calculator lets you calculate integrals and antiderivatives of functions online for free Our calculator allows you to check your solutions to calculus exercises It helps 1 Answer maganbhai P Aug 4 2018 I x 2 5 x2 5 2 arcsin x 5 c Explanation Here I 5 x2 1dx Using Integration by parts I 5 x2 1dx d dx 5

sqrt 5 x x 2 dx

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sqrt 5 x x 2 dx
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For the real values of x x2 we need x x2 0 0 x 1 If we put x sin2t where 0 t 2 1 x cos2t 0 1 x cost and dx 2sintcostdt So x x2dx x 1 x dx Our integral can be written as begin equation begin split int sqrt 5 4x x 2 dx int sqrt 9 4 4x x 2 dx int sqrt 3 2 x 2 2 dx end split

I was trying to solve int frac x 2 sqrt 5 4x 2 dx by using the substitution u sqrt 5 4x 2 dx frac sqrt 5 4x 2 4x du So the integral can Integrate x 2 sqrt 5 x 2 dx

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I 5 4x x2dx x 2 2 9dx From here let 3sin x 2 Thus 3cos d dx Plugging these in I 3 cos 9sin2 9d Factoring a 9 3 from the Integral of sqrt 16 5x 2 dx using trigonometric substitution calculus integral integrals integration trigonometricsubstitution

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sqrt 5 x x 2 dx - Our integral can be written as begin equation begin split int sqrt 5 4x x 2 dx int sqrt 9 4 4x x 2 dx int sqrt 3 2 x 2 2 dx end split