Final Answer
$-\cos\left(x\right)+\ln\left(x\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{x\cdot\sin\left(x\right)+1}{x}dx$
Specify the solving method
1
Expand the fraction $\frac{x\sin\left(x\right)+1}{x}$ into $2$ simpler fractions with common denominator $x$
$\int\left(\frac{x\sin\left(x\right)}{x}+\frac{1}{x}\right)dx$
Learn how to solve integral calculus problems step by step online.
$\int\left(\frac{x\sin\left(x\right)}{x}+\frac{1}{x}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int((xsin(x)+1)/x)dx. Expand the fraction \frac{x\sin\left(x\right)+1}{x} into 2 simpler fractions with common denominator x. Simplify. Expand the integral \int\left(\sin\left(x\right)+\frac{1}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sin\left(x\right)dx results in: -\cos\left(x\right).
Final Answer
$-\cos\left(x\right)+\ln\left(x\right)+C_0$