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Popular Calculus Problems

derivative of (x^2-4x+2)/(x+3)	derivative\:\frac{x^{2}-4x+2}{x+3}
limit as x approaches 1 of sqrt(x^2-1)	\lim\:_{x\to\:1}(\sqrt{x^{2}-1})
integral of 3x^2-5	\int\:3x^{2}-5dx
inverse oflaplace (e^{1-s})/(s^2-1)	inverselaplace\:\frac{e^{1-s}}{s^{2}-1}
taylor (e^{x^2}-1)/(x^2)	taylor\:\frac{e^{x^{2}}-1}{x^{2}}
derivative of (x^{1/3}+x/(ln(x)+x))	\frac{d}{dx}(\frac{x^{\frac{1}{3}}+x}{\ln(x)+x})
tangent of y= 2/(sqrt(x)),(1/16 ,8)	tangent\:y=\frac{2}{\sqrt{x}},(\frac{1}{16},8)
derivative of (3x^6)/(cos(x)e^x)	derivative\:\frac{3x^{6}}{\cos(x)e^{x}}
area x^2, 1/2 x^2,3x	area\:x^{2},\frac{1}{2}x^{2},3x
tangent of f(x)=x^2-3,(-2,1)	tangent\:f(x)=x^{2}-3,(-2,1)
integral of 1/(x^{1/2)-4}	\int\:\frac{1}{x^{\frac{1}{2}}-4}dx
integral of x^2sqrt(5-2x^3)	\int\:x^{2}\sqrt{5-2x^{3}}dx
integral of (x^{1.8}+11x^{4.5})	\int\:(x^{1.8}+11x^{4.5})dx
(\partial)/(\partial y)(7e^xln(y))	\frac{\partial\:}{\partial\:y}(7e^{x}\ln(y))
limit as x approaches 6 of x(x-3)	\lim\:_{x\to\:6}(x(x-3))
y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1	y^{\prime\:\prime\:}-18y^{\prime\:}+130y=0,y(0)=0,y(\frac{π}{2})=1
integral of (3x^2+3x+3)/(x^2+1)	\int\:\frac{3x^{2}+3x+3}{x^{2}+1}dx
derivative of x^2+4/x-10	\frac{d}{dx}(x^{2}+\frac{4}{x}-10)
derivative of (100/(x^5))	\frac{d}{dx}(\frac{100}{x^{5}})
integral of 3e^x-2cos(x)	\int\:3e^{x}-2\cos(x)dx
integral of 5/(x^2)	\int\:\frac{5}{x^{2}}dx
derivative of sqrt(1+1/(3x))	\frac{d}{dx}(\sqrt{1+\frac{1}{3x}})
derivative of (x^2/(x^2+5))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+5})
derivative of sqrt(11+tan^2(x))	derivative\:\sqrt{11+\tan^{2}(x)}
sum from n=0 to infinity of p(1-p)^n	\sum\:_{n=0}^{\infty\:}p(1-p)^{n}
taylor e^{-x^2}cos(x)	taylor\:e^{-x^{2}}\cos(x)
integral of e^{2x}*sin(3x)	\int\:e^{2x}\cdot\:\sin(3x)dx
derivative of csc^4(x)	\frac{d}{dx}(\csc^{4}(x))
derivative of (e^{2x}/x)	\frac{d}{dx}(\frac{e^{2x}}{x})
sum from n=0 to infinity of 5/(n!)	\sum\:_{n=0}^{\infty\:}\frac{5}{n!}
derivative of 1/(x^2+9)	\frac{d}{dx}(\frac{1}{x^{2}+9})
slope of (3,-6),(5,-5)	slope\:(3,-6),(5,-5)
area y=x^3-1,y=x-1	area\:y=x^{3}-1,y=x-1
limit as x approaches 1 of x+3ex-1+1	\lim\:_{x\to\:1}(x+3ex-1+1)
derivative of 1.8^{2x}	derivative\:1.8^{2x}
inverse oflaplace ((2s+1))/(s^2+2s+1)	inverselaplace\:\frac{(2s+1)}{s^{2}+2s+1}
y^'=x^2	y^{\prime\:}=x^{2}
sum from n=1 to infinity of 5/(4^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{5}{4^{n+1}}
derivative of cos(6x^3)	\frac{d}{dx}(\cos(6x^{3}))
(1+y^2)dx+(1+x^2)dy=0	(1+y^{2})dx+(1+x^{2})dy=0
laplacetransform t-5	laplacetransform\:t-5
tangent of f(x)= 8/(x^2),\at x=2	tangent\:f(x)=\frac{8}{x^{2}},\at\:x=2
limit as x approaches-2 of (x^2+5x+6)/x	\lim\:_{x\to\:-2}(\frac{x^{2}+5x+6}{x})
integral of (2x+18)/(x^2+10x+24)	\int\:\frac{2x+18}{x^{2}+10x+24}dx
derivative of y=ln(9+x^2)	derivative\:y=\ln(9+x^{2})
derivative of ((x^2+2x/(sin(x)))^3)	\frac{d}{dx}((\frac{x^{2}+2x}{\sin(x)})^{3})
integral of x^{-13}	\int\:x^{-13}dx
integral of 1/(x^2sqrt(x^2-49))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-49}}dx
integral of (1/(x(x-4)))	\int\:(\frac{1}{x(x-4)})dx
integral of (2x^2)/(1-2x^3)	\int\:\frac{2x^{2}}{1-2x^{3}}dx
tangent of f(x)=(12x-3)^{1/2},\at x=1	tangent\:f(x)=(12x-3)^{\frac{1}{2}},\at\:x=1
limit as x approaches-infinity of e^x-x	\lim\:_{x\to\:-\infty\:}(e^{x}-x)
derivative of cot^2(5x)	\frac{d}{dx}(\cot^{2}(5x))
derivative of cos(3sin(x))	\frac{d}{dx}(\cos(3\sin(x)))
(d^2)/(dx^2)y+49y=0	\frac{d^{2}}{dx^{2}}y+49y=0
derivative of (3x-1^2)	\frac{d}{dx}((3x-1)^{2})
limit as x approaches 7 of ((x+7))/(x-7)	\lim\:_{x\to\:7}(\frac{(x+7)}{x-7})
sum from n=0 to infinity}(-2)^{3-2n of*3	\sum\:_{n=0}^{\infty\:}(-2)^{3-2n}\cdot\:3
derivative of 2^x	derivative\:2^{x}
limit as x approaches 4 of 7*a+x	\lim\:_{x\to\:4}(7\cdot\:a+x)
integral of xe^{1-x^2}	\int\:xe^{1-x^{2}}dx
derivative of ln(3x^2-5)	\frac{d}{dx}(\ln(3x^{2}-5))
derivative of \| 1/x \|	\frac{d}{dx}(\left\|\frac{1}{x}\right\|)
integral of x(x+2)	\int\:x(x+2)dx
integral from 0 to 1 of 6^{3x}	\int\:_{0}^{1}6^{3x}dx
integral of (sqrt(x^2-49))/(x^3)	\int\:\frac{\sqrt{x^{2}-49}}{x^{3}}dx
(\partial)/(\partial x)(4xye^x)	\frac{\partial\:}{\partial\:x}(4xye^{x})
limit as x approaches 2 of 3x^4+2x^2-x+1	\lim\:_{x\to\:2}(3x^{4}+2x^{2}-x+1)
limit as x approaches-8 of x^3	\lim\:_{x\to\:-8}(x^{3})
y^{''}+25y=e^{-t}	y^{\prime\:\prime\:}+25y=e^{-t}
sum from k=1 to infinity of 1/(k(k+1))	\sum\:_{k=1}^{\infty\:}\frac{1}{k(k+1)}
integral of 0.02e^{-0.02x}	\int\:0.02e^{-0.02x}dx
derivative of (8x^2+2x+4)/(sqrt(x))	derivative\:\frac{8x^{2}+2x+4}{\sqrt{x}}
1/4 q^{''}+10q^'+1000q=0	\frac{1}{4}q^{\prime\:\prime\:}+10q^{\prime\:}+1000q=0
limit as x approaches 0+of (1+x)^{7/x}	\lim\:_{x\to\:0+}((1+x)^{\frac{7}{x}})
integral of (2x^5-4sqrt(x)+8x)/x	\int\:\frac{2x^{5}-4\sqrt{x}+8x}{x}dx
maclaurin ln(1+e^x)	maclaurin\:\ln(1+e^{x})
derivative of arcsin(2x^4)	\frac{d}{dx}(\arcsin(2x^{4}))
integral of (x^2+4x+7)/(x^2-6x+5)	\int\:\frac{x^{2}+4x+7}{x^{2}-6x+5}dx
integral from 0 to t of e^{-x}	\int\:_{0}^{t}e^{-x}dx
integral of (((x^3+1)^2)/(x^2))	\int\:(\frac{(x^{3}+1)^{2}}{x^{2}})dx
(\partial)/(\partial x)(xyln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(xy\ln(x^{2}+y^{2}))
derivative of ln(cosh(3x))	\frac{d}{dx}(\ln(\cosh(3x)))
limit as x approaches pi/4 of (sin(2x)-1)/(4x-pi)	\lim\:_{x\to\:\frac{π}{4}}(\frac{\sin(2x)-1}{4x-π})
derivative of cos(2x+3y)	\frac{d}{dx}(\cos(2x+3y))
y^{''}-16y^'+63y=240e^x	y^{\prime\:\prime\:}-16y^{\prime\:}+63y=240e^{x}
integral of (x-5)/(x^2+2x-3)	\int\:\frac{x-5}{x^{2}+2x-3}dx
tangent of f(x)= 3/(5x+2),\at x=-1	tangent\:f(x)=\frac{3}{5x+2},\at\:x=-1
integral of (2x+1)^{5/6}	\int\:(2x+1)^{\frac{5}{6}}dx
(\partial)/(\partial x)(32x+13y+90)	\frac{\partial\:}{\partial\:x}(32x+13y+90)
d/(dt)(ln(a+{v}(t)t))	\frac{d}{dt}(\ln(a+{v}(t)t))
derivative of (-1^nx^{2n})	\frac{d}{dx}((-1)^{n}x^{2n})
y^'=0.5y,y(2)=100	y^{\prime\:}=0.5y,y(2)=100
limit as x approaches-1 of (\|x+1\|)/(x+1)	\lim\:_{x\to\:-1}(\frac{\left\|x+1\right\|}{x+1})
integral from 1 to 2 of (2x+1)ln(x)	\int\:_{1}^{2}(2x+1)\ln(x)dx
integral of (x^2+1)/(x^3+3x-16)	\int\:\frac{x^{2}+1}{x^{3}+3x-16}dx
integral of sqrt(e^{2t)+e^{-2t}+2}	\int\:\sqrt{e^{2t}+e^{-2t}+2}dt
integral of xln(x^2+1)	\int\:x\ln(x^{2}+1)dx
inverse oflaplace 1/(s^2(s+1.1))	inverselaplace\:\frac{1}{s^{2}(s+1.1)}
integral of 1/(sqrt(2+x-x^2))	\int\:\frac{1}{\sqrt{2+x-x^{2}}}dx

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