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)

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

\frac{\partial}{\partial y} (3 x^{2} + 2 x y^{3})

n = 1 \sum \infty \frac{x ^{n}}{6 ^{n}}

\int tan (x) y d y

ln (14 - 9 x^{2} + 2 x^{4})

\frac{d}{d x} (\frac{2 x ^{2} + 4 x}{2 + x ^{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