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Find the integral $\int\frac{x\sin\left(x\right)+1}{x}dx$

Step-by-step Solution

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Solution

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Final Answer

$-\cos\left(x\right)+\ln\left(x\right)+C_0$
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Step-by-step Solution

Problem to solve:

$\int\frac{x\sin\left(x\right)+1}{x}dx$

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.

$\int\left(\frac{x\sin\left(x\right)}{x}+\frac{1}{x}\right)dx$

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Unlock the first 2 steps of this solution.

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 the resulting fractions. 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

$-\cos\left(x\right)+\ln\left(x\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int((xsin(x)+1)/x)dx using basic integralsSolve int((xsin(x)+1)/x)dx using u-substitutionSolve int((xsin(x)+1)/x)dx using integration by partsSolve int((xsin(x)+1)/x)dx using tabular integration

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◻/◻
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◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main topic:

Integral Calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.04 s

Related topics:

Integral CalculusCalculus

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