Evaluate
С+e^{w}-3w
Differentiate w.r.t. w
e^{w}-3
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\int e^{w}\mathrm{d}w+\int -3\mathrm{d}w
Integrate the sum term by term.
e^{w}+\int -3\mathrm{d}w
Use \int e^{w}\mathrm{d}w=e^{w} from the table of common integrals to obtain the result.
e^{w}-3w
Find the integral of -3 using the table of common integrals rule \int a\mathrm{d}w=aw.
e^{w}-3w+С
If F\left(w\right) is an antiderivative of f\left(w\right), then the set of all antiderivatives of f\left(w\right) is given by F\left(w\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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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
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