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Popular Calculus Problems

integral from 0 to infinity of 3e^{2x}	\int\:_{0}^{\infty\:}3e^{2x}dx
limit as y approaches 0 of (4y^5+5y^3)/(y^4-y)	\lim\:_{y\to\:0}(\frac{4y^{5}+5y^{3}}{y^{4}-y})
integral of-x/(1+x)	\int\:-\frac{x}{1+x}dx
area 6-y=x^2,y+8=x^2,x-y+4=0,x-y-6=0	area\:6-y=x^{2},y+8=x^{2},x-y+4=0,x-y-6=0
y^{''}-7y^'+12y=0,y(0)=-2,y^'(0)=4	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=0,y(0)=-2,y^{\prime\:}(0)=4
derivative of 1/(sqrt(x+sin(x)))	\frac{d}{dx}(\frac{1}{\sqrt{x+\sin(x)}})
(dy)/(dx)=(4e^{4x})/(e^y)	\frac{dy}{dx}=\frac{4e^{4x}}{e^{y}}
integral of 2e^{-st}	\int\:2e^{-st}dt
inverse oflaplace ((s-1))/(s^2+2s+2)	inverselaplace\:\frac{(s-1)}{s^{2}+2s+2}
limit as x approaches infinity of 3-f(x)	\lim\:_{x\to\:\infty\:}(3-f(x))
tangent of 8x^3-36x^2-96	tangent\:8x^{3}-36x^{2}-96
derivative of 2arcsec(sqrt(x))	\frac{d}{dx}(2\arcsec(\sqrt{x}))
integral of e^{5x}cos(7x)	\int\:e^{5x}\cos(7x)dx
slope of (3,8),(7,-7)	slope\:(3,8),(7,-7)
limit as x approaches 3+of 1-x	\lim\:_{x\to\:3+}(1-x)
integral from 1 to 4 of 2pix(e^x-ln(x))	\int\:_{1}^{4}2πx(e^{x}-\ln(x))dx
(4arccos(sqrt(1-x^2)))^'	(4\arccos(\sqrt{1-x^{2}}))^{\prime\:}
derivative of sqrt(x^2+y^2-9)	\frac{d}{dx}(\sqrt{x^{2}+y^{2}-9})
derivative of sin^2(x-cos(2x))	\frac{d}{dx}(\sin^{2}(x)-\cos(2x))
limit as x approaches 4+of 5	\lim\:_{x\to\:4+}(5)
integral of sin(ln(14x))	\int\:\sin(\ln(14x))dx
derivative of (x/(2(x^2-1)^2-1))^2	derivative\:(\frac{x}{2(x^{2}-1)^{2}-1})^{2}
integral from 0 to 30 of 4x(30-x)	\int\:_{0}^{30}4x(30-x)dx
(\partial)/(\partial x)(x^3e^{sqrt(4xy)})	\frac{\partial\:}{\partial\:x}(x^{3}e^{\sqrt{4xy}})
y^'= y/t-1/(y/t)	y^{\prime\:}=\frac{y}{t}-\frac{1}{\frac{y}{t}}
tangent of f(x)=x+2/x ,\at x=2	tangent\:f(x)=x+\frac{2}{x},\at\:x=2
integral of (50)/(x^{0.25)}	\int\:\frac{50}{x^{0.25}}dx
d/(dy)(xe^{x-y})	\frac{d}{dy}(xe^{x-y})
integral from 0 to 6 of pi(3x)^2	\int\:_{0}^{6}π(3x)^{2}dx
integral of ((ln(u))^8)/u	\int\:\frac{(\ln(u))^{8}}{u}du
(dy}{dx}=\frac{e^{3x}+3xy+y)/x	\frac{dy}{dx}=\frac{e^{3x}+3xy+y}{x}
(d^2)/(dx^2)((3x-2)/(2x+1))	\frac{d^{2}}{dx^{2}}(\frac{3x-2}{2x+1})
derivative of (log_{3}(x)/(log_{7)(x)})	\frac{d}{dx}(\frac{\log_{3}(x)}{\log_{7}(x)})
integral of x^2-cos(x)	\int\:x^{2}-\cos(x)dx
dx+e^{5x}dy=0	dx+e^{5x}dy=0
laplacetransform s^2+2s+1	laplacetransform\:s^{2}+2s+1
derivative of y=x^2e^x-2xe^x+4e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+4e^{x}
integral of (x-pi)sin(x)	\int\:(x-π)\sin(x)dx
integral from 0 to 5 of 1	\int\:_{0}^{5}1dx
y^{''}+y^'-6y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=1
derivative of 1+2x^2	derivative\:1+2x^{2}
derivative of ln(3+sqrt(x))	derivative\:\ln(3+\sqrt{x})
(dy)/(dx)+y=e^{4x}	\frac{dy}{dx}+y=e^{4x}
derivative of-(2x+3/((x^2+3x+2)^2))	\frac{d}{dx}(-\frac{2x+3}{(x^{2}+3x+2)^{2}})
limit as x approaches 3 of 3x-7	\lim\:_{x\to\:3}(3x-7)
derivative of 1/(x^7)	derivative\:\frac{1}{x^{7}}
limit as x approaches 0+of e^x-(1+x)	\lim\:_{x\to\:0+}(e^{x}-(1+x))
(\partial)/(\partial x)(x*arccsc(x/2))	\frac{\partial\:}{\partial\:x}(x\cdot\:\arccsc(\frac{x}{2}))
integral of sqrt(5x^2+1)	\int\:\sqrt{5x^{2}+1}dx
integral of (ae^x+b)/(ae^x-b)	\int\:\frac{ae^{x}+b}{ae^{x}-b}dx
(9xy^2-4y)+(9x^2y-4x)y^'=0	(9xy^{2}-4y)+(9x^{2}y-4x)y^{\prime\:}=0
integral of (csc(3x)-cot(3x))^2	\int\:(\csc(3x)-\cot(3x))^{2}dx
y^{''}-2y^'=sin(x),y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}=\sin(x),y(0)=1,y^{\prime\:}(0)=2
integral of sqrt(t^2+4)	\int\:\sqrt{t^{2}+4}dt
derivative of sin(x+5/6 cot(x))	\frac{d}{dx}(\sin(x)+\frac{5}{6}\cot(x))
integral from-8 to 0 of (4-9x)^{-0.5}	\int\:_{-8}^{0}(4-9x)^{-0.5}dx
area (x-1)^3,(x-1)	area\:(x-1)^{3},(x-1)
(\partial)/(\partial x)(1/2 ln(x^2d))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(x^{2}d))
derivative of sqrt(csc(x))	\frac{d}{dx}(\sqrt{\csc(x)})
integral of 15cos(15x)	\int\:15\cos(15x)dx
derivative of f(x)=9x-10x^{1/4}	derivative\:f(x)=9x-10x^{\frac{1}{4}}
integral of 1/(cos(y))	\int\:\frac{1}{\cos(y)}dy
integral from 0 to 0.75 of 2x	\int\:_{0}^{0.75}2xdx
derivative of Ax^{-1/2}	\frac{d}{dx}(Ax^{-\frac{1}{2}})
area x=y 1/3 ,x=0,y=64	area\:x=y\frac{1}{3},x=0,y=64
(y^2+yx)dx+x^2dy=0	(y^{2}+yx)dx+x^{2}dy=0
derivative of (4x^5)/(e^{3x)}	derivative\:\frac{4x^{5}}{e^{3x}}
limit as x approaches 0-of (e^x)/(1-e^x)	\lim\:_{x\to\:0-}(\frac{e^{x}}{1-e^{x}})
derivative of f(x)=e^{-x}x-2e^{-x}	derivative\:f(x)=e^{-x}x-2e^{-x}
(\partial)/(\partial x)(cos(8xy))	\frac{\partial\:}{\partial\:x}(\cos(8xy))
derivative of y=2x+8	derivative\:y=2x+8
integral of sqrt(1+36x)	\int\:\sqrt{1+36x}dx
derivative of \sqrt[3]{x^2}(2x-x^2)	\frac{d}{dx}(\sqrt[3]{x^{2}}(2x-x^{2}))
d/(dt)(ae^{bt})	\frac{d}{dt}(ae^{bt})
(\partial)/(\partial x)(e^{-t})	\frac{\partial\:}{\partial\:x}(e^{-t})
derivative of 1/x+1/(x^2)	\frac{d}{dx}(\frac{1}{x}+\frac{1}{x^{2}})
(\partial)/(\partial t)(sech^2(x-t))	\frac{\partial\:}{\partial\:t}(\sech^{2}(x-t))
integral of 6x^4e^{x^5}	\int\:6x^{4}e^{x^{5}}dx
derivative of (2x^2-2xle{f}(x,t)t(x^2-3))	\frac{d}{dx}((2x^{2}-2x)le{f}(x,t)t(x^{2}-3))
derivative of f(x)=(2+5x)^2	derivative\:f(x)=(2+5x)^{2}
limit as x approaches 0+of 1/x-1/(x^2+x)	\lim\:_{x\to\:0+}(\frac{1}{x}-\frac{1}{x^{2}+x})
(\partial)/(\partial x)(xy^2-x^2y+xy)	\frac{\partial\:}{\partial\:x}(xy^{2}-x^{2}y+xy)
integral from 0 to 2 of 8e^{-3x}	\int\:_{0}^{2}8e^{-3x}dx
limit as x approaches-3 of sqrt(9-x^2)	\lim\:_{x\to\:-3}(\sqrt{9-x^{2}})
sum from k=0 to infinity of 3(x/4)^k	\sum\:_{k=0}^{\infty\:}3(\frac{x}{4})^{k}
simplify ((x^2+1)/(x^2-1))^3	simplify\:(\frac{x^{2}+1}{x^{2}-1})^{3}
limit as h approaches 0 of 3h+6	\lim\:_{h\to\:0}(3h+6)
limit as x approaches 0 of (cos(4x^2))/x	\lim\:_{x\to\:0}(\frac{\cos(4x^{2})}{x})
integral of 5/(sqrt(3-4x-x^2))	\int\:\frac{5}{\sqrt{3-4x-x^{2}}}dx
taylor xln(x),1	taylor\:x\ln(x),1
limit as x approaches 0 of arctan(x^2+1)	\lim\:_{x\to\:0}(\arctan(x^{2}+1))
integral from 0 to 1 of integral from 0 to 2 of xye^{xy^2}	\int\:_{0}^{1}\int\:_{0}^{2}xye^{xy^{2}}dxdy
integral of (e^{2x}+4)^{-1}	\int\:(e^{2x}+4)^{-1}dx
integral from ln(4) to ln(25) of e^{x/2}	\int\:_{\ln(4)}^{\ln(25)}e^{\frac{x}{2}}dx
limit as x approaches 0 of-5/(1-5x)	\lim\:_{x\to\:0}(-\frac{5}{1-5x})
(dy)/(dx)= 1/(sqrt(1-x)),y(0)=1	\frac{dy}{dx}=\frac{1}{\sqrt{1-x}},y(0)=1
derivative of f(x)=(x^2+2x-4)/((x+1)^2)	derivative\:f(x)=\frac{x^{2}+2x-4}{(x+1)^{2}}
tangent of x^3-x^2+1	tangent\:x^{3}-x^{2}+1
integral of x*ln((1-x)/(1+x))	\int\:x\cdot\:\ln(\frac{1-x}{1+x})dx
derivative of (ln(x+1)^{2-e^{x^2}})	\frac{d}{dx}((\ln(x+1))^{2-e^{x^{2}}})

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