Evaluate
\ln(|x|)+x+С
Differentiate w.r.t. x
1+\frac{1}{x}
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\int \frac{1}{x}\mathrm{d}x+\int 1\mathrm{d}x
Integrate the sum term by term.
\ln(|x|)+\int 1\mathrm{d}x
Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.
\ln(|x|)+x
Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.
\ln(|x|)+x+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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699 * 533
Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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