Evaluate
3x^{2}+4x+\frac{5}{4}
Expand
3x^{2}+4x+\frac{5}{4}
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3x^{2}+x\times \frac{5}{2}+\frac{1}{2}\times 3x+\frac{1}{2}\times \frac{5}{2}
Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of 3x+\frac{5}{2}.
3x^{2}+x\times \frac{5}{2}+\frac{3}{2}x+\frac{1}{2}\times \frac{5}{2}
Multiply \frac{1}{2} and 3 to get \frac{3}{2}.
3x^{2}+4x+\frac{1}{2}\times \frac{5}{2}
Combine x\times \frac{5}{2} and \frac{3}{2}x to get 4x.
3x^{2}+4x+\frac{1\times 5}{2\times 2}
Multiply \frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
3x^{2}+4x+\frac{5}{4}
Do the multiplications in the fraction \frac{1\times 5}{2\times 2}.
3x^{2}+x\times \frac{5}{2}+\frac{1}{2}\times 3x+\frac{1}{2}\times \frac{5}{2}
Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of 3x+\frac{5}{2}.
3x^{2}+x\times \frac{5}{2}+\frac{3}{2}x+\frac{1}{2}\times \frac{5}{2}
Multiply \frac{1}{2} and 3 to get \frac{3}{2}.
3x^{2}+4x+\frac{1}{2}\times \frac{5}{2}
Combine x\times \frac{5}{2} and \frac{3}{2}x to get 4x.
3x^{2}+4x+\frac{1\times 5}{2\times 2}
Multiply \frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
3x^{2}+4x+\frac{5}{4}
Do the multiplications in the fraction \frac{1\times 5}{2\times 2}.
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\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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