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Step-by-step Solution

Solve the trigonometric integral $\int x\cos\left(bx\right)dx$

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Step-by-step explanation

Problem to solve:

$\int_{ }^{ }x\cos bx\:dx$

Learn how to solve calculus 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 calculus problems step by step online. Solve the trigonometric integral int(x*cos(b*x))dx. Use the integration by parts theorem to calculate the integral \int x\cos\left(bx\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Answer

$\frac{x\sin\left(bx\right)+\frac{\cos\left(u\right)}{b}}{b}+C_0$

Problem Analysis

$\int_{ }^{ }x\cos bx\:dx$

Main topic:

Calculus

Related formulas:

2. See formulas

Time to solve it:

~ 2.24 seconds