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Step-by-step Solution

Solve the trigonometric integral $\int e^t\cos\left(t\right)dt$

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Step-by-step explanation

Problem to solve:

$\int\left(e^t\cos\left(t\right)\right)dt$

Learn how to solve trigonometric integrals problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock this full step-by-step solution!

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(2.718281828459045^t*cos(t))dt. Use the integration by parts theorem to calculate the integral \int e^t\cos\left(t\right)dt, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Answer

$\frac{1}{2}\left(e^t\sin\left(t\right)+e^t\cos\left(t\right)\right)+C_0$

Problem Analysis

$\int\left(e^t\cos\left(t\right)\right)dt$

Related formulas:

3. See formulas

Time to solve it:

~ 0.33 seconds