Step-by-step Solution

Integrate $\int\frac{\cos\left(x\right)}{x}dx$ with respect to x

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Step-by-step explanation

Problem to solve:

$\int\frac{\cos\left(x\right)}{x}dx$

Learn how to solve calculus problems step by step online.

$\int\frac{\sum_{n=0}^{\infty } x^{2n}\frac{{\left(-1\right)}^n}{\left(2n\right)!}}{x}dx$

Unlock this full step-by-step solution!

Learn how to solve calculus problems step by step online. Integrate int(((cos(x)/x))dx with respect to x. Rewrite the function \cos\left(x\right) as it's representation in Maclaurin series expansion. Rewriting the exponent. Applying the power of a power property. Bring the denominator x inside the power serie.

Final Answer

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n\right)!}\frac{x^{2n}}{2n}+C_0$

Problem Analysis

$\int\frac{\cos\left(x\right)}{x}dx$

Main topic:

Calculus

Related formulas:

2. See formulas

Time to solve it:

~ 0.11 seconds