Evaluate
\frac{y\sqrt{x^{2}+4x-1}}{4x}+С
Differentiate w.r.t. x
-\frac{y\left(2x-1\right)}{4\sqrt{\left(x-\left(-\sqrt{5}-2\right)\right)\left(x-\left(\sqrt{5}-2\right)\right)}x^{2}}
Share
Copied to clipboard
\frac{\sqrt{4x+x^{2}-1}}{4x}y
Find the integral of \frac{\sqrt{4x+x^{2}-1}}{4x} using the table of common integrals rule \int a\mathrm{d}y=ay.
\frac{\sqrt{4x+x^{2}-1}y}{4x}
Simplify.
\frac{\sqrt{4x+x^{2}-1}y}{4x}+С
If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}