What is taylor e^x*cos(x) ?

The answer to taylor e^x*cos(x) is 1+x-1/3 x^3-1/6 x^4-1/30 x^5+\ldots

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taylor e^x*cos(x)

taylor

e^{x} \cdot cos (x)

1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

\int_{- 1}^{1} (\frac{1}{1 + x ^{2}})^{2} d x

\int \frac{3 x ^{3} - 4 x ^{2} + 3 x}{x ^{2} + 1} d x

\int 6 x^{5} - 7 x^{4} - 9 x^{2} d x

\int x + c d x

\int_{0}^{1} \int_{0}^{x} (\frac{6}{7} (x^{2} + x \cdot \frac{y}{2})) d y d x

What is taylor e^x*cos(x) ?
The answer to taylor e^x*cos(x) is 1+x-1/3 x^3-1/6 x^4-1/30 x^5+\ldots