What is the integral of e^xcos^2(x) ?

The integral of e^xcos^2(x) is e^xcos^2(x)-2/5 e^xcos(2x)+1/5 e^xsin(2x)+C

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integral of e^xcos^2(x)

integral

e^{x} cos^{2} (x)

e^{x} cos^{2} (x) - \frac{2}{5} e^{x} cos (2 x) + \frac{1}{5} e^{x} sin (2 x) + C

Solution steps

\int e^{x} cos^{2} (x) d x

Apply Integration By Parts

: e^{x} cos^{2} (x) - \int - e^{x} sin (2 x) d x

= e^{x} cos^{2} (x) - \int - e^{x} sin (2 x) d x

\int - e^{x} sin (2 x) d x = \frac{2}{5} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

= e^{x} cos^{2} (x) - (\frac{2}{5} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x))

Simplify

= e^{x} cos^{2} (x) - \frac{2}{5} e^{x} cos (2 x) + \frac{1}{5} e^{x} sin (2 x)

Add a constant to the solution

= e^{x} cos^{2} (x) - \frac{2}{5} e^{x} cos (2 x) + \frac{1}{5} e^{x} sin (2 x) + C

y = cos (x^{2}) (0.1)

t^{2} (e^{t})^{2}

4 x^{10}

\frac{1}{x} + \frac{1}{e ^{x}}

\frac{r ^{2}}{( 1 + r ^{2} )}

What is the integral of e^xcos^2(x) ?
The integral of e^xcos^2(x) is e^xcos^2(x)-2/5 e^xcos(2x)+1/5 e^xsin(2x)+C