What is taylor x*sin(x)+x*cos(x) ?

The answer to taylor x*sin(x)+x*cos(x) is x+x^2-1/2 x^3-1/6 x^4+1/24 x^5+\ldots

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taylor xsin(x)+xcos(x)

taylor

x \cdot sin (x) + x \cdot cos (x)

x + x^{2} - \frac{1}{2} x^{3} - \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x sin ( x ) + x cos ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x sin ( x ) + x cos ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x sin ( x ) + x cos ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{2}{2 !} x^{2} + \frac{- 3}{3 !} x^{3} + \frac{- 4}{4 !} x^{4} + \frac{5}{5 !} x^{5} + \dots

Refine

= x + x^{2} - \frac{1}{2} x^{3} - \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

\int 2 x^{- 1} d x

{\frac{1}{s ^{2}} - \frac{1}{s} + \frac{1}{s - 2}}

\int (\frac{y}{x} + 6 x) d x

\int_{0}^{\frac{π}{2}} 10 cos^{5} (x) d x

\int 3 x^{\frac{4}{3}} - sin (x) + c d x

What is taylor x*sin(x)+x*cos(x) ?
The answer to taylor x*sin(x)+x*cos(x) is x+x^2-1/2 x^3-1/6 x^4+1/24 x^5+\ldots