What is the integral of e^xcos(4y) ?

The integral of e^xcos(4y) is cos(4y)e^x+C

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integral of e^xcos(4y)

\int e^{x} cos (4 y) d x

cos (4 y) e^{x} + C

Solution steps

\int e^{x} cos (4 y) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (4 y) \cdot \int e^{x} d x

Use the common integral:

\int e^{x} d x = e^{x}

= cos (4 y) e^{x}

Add a constant to the solution

= cos (4 y) e^{x} + C

x \to 1 lim (ln (x - 1))

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

\int (x + 1) e^{2 x} d x

3 x^{\frac{1}{2}}

f (x) = 3 x cos (x), at x = π