Evaluate the integrals in Exercises 1–24 using integration by parts.
∫ e^(-y) cos(y) dy

Guida verificata passo dopo passo

Identify the integral to solve: $\int e^{-y} \cos(y) \, dy$.

Recall the integration by parts formula: $\int u \, dv = uv - \int v \, du$.

Choose $u$ and $dv$ wisely. For this integral, let $u = \cos(y)$ and $dv = e^{-y} dy$.

Compute $du$ and $v$: differentiate $u$ to get $du = -\sin(y) dy$, and integrate $dv$ to get $v = \int e^{-y} dy = -e^{-y}$.

Apply the integration by parts formula: substitute $u$, $v$, $du$ into $\int u \, dv = uv - \int v \, du$ and simplify the resulting integral.

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