What is maclaurin e^xsin(x) ?

The answer to maclaurin e^xsin(x) is x+x^2+1/3 x^3-1/30 x^5-1/90 x^6+\ldots

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maclaurin e^xsin(x)

maclaurin

e^{x} sin (x)

x + x^{2} + \frac{1}{3} x^{3} - \frac{1}{30} x^{5} - \frac{1}{90} x^{6} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{2}{2 !} x^{2} + \frac{2}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 4}{5 !} x^{5} + \frac{- 8}{6 !} x^{6} + \dots

Refine

= x + x^{2} + \frac{1}{3} x^{3} - \frac{1}{30} x^{5} - \frac{1}{90} x^{6} + \dots

\int \frac{5 - e ^{x}}{e ^{2 x}} d x

\int \frac{1}{( 64 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{220 x}{( x + 2 ) ^{2}}

\int (1 - \frac{3}{y} + x) d y

\int_{1}^{4} (x^{3} + \frac{1}{4 x ^{3}}) d x

What is maclaurin e^xsin(x) ?
The answer to maclaurin e^xsin(x) is x+x^2+1/3 x^3-1/30 x^5-1/90 x^6+\ldots