int 1 1 x 4 x 2 dx Enter the function you want to integrate into the Integral Calculator Skip the f x part and the differential dx The Integral Calculator will show you a graphical version of your input while you type Make sure that it shows exactly what you
The indefinite integral is a rational fraction and is typically solved using partial fractions decomposition You first factor the denominator x4 1 which has four complex roots the int x 2 1 x 4 x 2 1 dx int 1 1 x 2 x 2 1 1 x 2 dx int 1 1 x 2 dx x 1 x 2 1 After using y x 1 x and dy 1 1 x 2 dx transforms this integral became int dy y 2 1 1 2int 2dy y 1 y 1
int 1 1 x 4 x 2 dx
int 1 1 x 4 x 2 dx
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int 1 x 2 x 1 2x dx YouTube
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int 1 x 2 1 2 dx YouTube
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x 4 x 2 1 x 2 1 1 x 2 1 So int x 4dx x 2 1 int x 2 1 dx color red intdx x 2 1 x 3 3 x color red intdx x 2 1 The integral in red is int1 1 4x 2 dx 1 2int sec 2 u 1 tan 2 du du Now using the trig identity on the bottom of the fraction we get 1 2intsec 2 u sec 2 u du 1 2int du Integrating then
int infty infty x 4 e x 2 2 dx I am working on something related to the moments of normal distribution and require the evaluation of the above integral I can get the answer from Integral Calculator Calculator integrates functions using various methods common integrals substitution integration by parts partial fraction decomposition trigonometric hyperbolic logarithmic identities and formulas
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If so note that frac x 4 1 x 4 1 x 2 x 4 x 1 2 left 1 frac 2x 1 x 2 right while you can use int frac 2x 1 x 2 ln 1 x 2 c and int frac 1 1 x 2 arctan x c to Add a constant to the solution mathrm If frac dF x dx f x mathrm then int f x dx F x C Power Rule int x a dx frac x a 1 a 1 quad a ne 1 Integral
Series expansion of the integral at x Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math int x 4 1 x 2 1 dx int x 2 1 x 2 1 x 2 1 dx int x 2 1 dx x 3 3 x c
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int 1 1 x 4 x 2 dx - int infty infty x 4 e x 2 2 dx I am working on something related to the moments of normal distribution and require the evaluation of the above integral I can get the answer from