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Popular Calculus Problems

integral of x^2-3x+4	\int\:x^{2}-3x+4dx
limit as x approaches 0+of sin(x)ln(7x)	\lim\:_{x\to\:0+}(\sin(x)\ln(7x))
integral of (e^x-4e^{-x})/(e^x)	\int\:\frac{e^{x}-4e^{-x}}{e^{x}}dx
y^3-(10x+2)+3xy^2(dy)/(dx)=0	y^{3}-(10x+2)+3xy^{2}\frac{dy}{dx}=0
(\partial)/(\partial x)(xe^y+y+1)	\frac{\partial\:}{\partial\:x}(xe^{y}+y+1)
(\partial}{\partial y}(\frac{x^2-y^2)/2)	\frac{\partial\:}{\partial\:y}(\frac{x^{2}-y^{2}}{2})
integral from 0 to 0.02 of 200x	\int\:_{0}^{0.02}200xdx
inverse oflaplace (3s+1)/(s(s+2))	inverselaplace\:\frac{3s+1}{s(s+2)}
tangent of 1/(2x+2),\at x=5	tangent\:\frac{1}{2x+2},\at\:x=5
(4-x^2)(dy)/(dx)=2y	(4-x^{2})\frac{dy}{dx}=2y
tangent of y=((x+1)/(x-3))^2,(7,4)	tangent\:y=(\frac{x+1}{x-3})^{2},(7,4)
integral of 2cos^2(x/2)	\int\:2\cos^{2}(\frac{x}{2})dx
integral of 1/(tln(t))	\int\:\frac{1}{t\ln(t)}dt
tangent of y=5e^x+x,(0,5)	tangent\:y=5e^{x}+x,(0,5)
integral of 1/(49-64x^2)	\int\:\frac{1}{49-64x^{2}}dx
integral of t^7e^{-t^4}	\int\:t^{7}e^{-t^{4}}dt
derivative of (3x^4+3/(sin(x)))	\frac{d}{dx}(\frac{3x^{4}+3}{\sin(x)})
d/(ds)(sqrt(s^2+t^2))	\frac{d}{ds}(\sqrt{s^{2}+t^{2}})
tangent of 3x^4-7x^2,\at x=-1	tangent\:3x^{4}-7x^{2},\at\:x=-1
integral of (-2x+4)/((x^2+1)(x-1)^2)	\int\:\frac{-2x+4}{(x^{2}+1)(x-1)^{2}}dx
limit as x approaches-3 of 1/2-x^3	\lim\:_{x\to\:-3}(\frac{1}{2}-x^{3})
derivative of 2x^3+3x^2-120x	\frac{d}{dx}(2x^{3}+3x^{2}-120x)
(dv)/(dy)=(v-y^3)/(v-y)	\frac{dv}{dy}=\frac{v-y^{3}}{v-y}
derivative of f(x)=sqrt(25-x^2)	derivative\:f(x)=\sqrt{25-x^{2}}
x(4x+2y)y^'+y(12x+2y)=0	x(4x+2y)y^{\prime\:}+y(12x+2y)=0
integral from-1 to 1 of e^y-y^2-2	\int\:_{-1}^{1}e^{y}-y^{2}-2dy
tangent of y=x^4+3x^3-2x-2	tangent\:y=x^{4}+3x^{3}-2x-2
derivative of log_{5}(sqrt(x^2-1))	derivative\:\log_{5}(\sqrt{x^{2}-1})
limit as x approaches 1 of-x^2-1	\lim\:_{x\to\:1}(-x^{2}-1)
integral of (4x+1)^{-1/2}	\int\:(4x+1)^{-\frac{1}{2}}dx
integral of 20xe^{8x}	\int\:20xe^{8x}dx
(dy)/(dt)= y/(t+1)+4t^2+4t	\frac{dy}{dt}=\frac{y}{t+1}+4t^{2}+4t
derivative of (2x^2/3-sin(x)+3)	\frac{d}{dx}(\frac{2x^{2}}{3}-\sin(x)+3)
limit as x approaches 2 of (x-3)/(x^2+1)	\lim\:_{x\to\:2}(\frac{x-3}{x^{2}+1})
integral of sin^2(xco)s^5x	\int\:\sin^{2}(xco)s^{5}xdx
integral of ax(x-4)	\int\:ax(x-4)dx
integral of xln(2)	\int\:x\ln(2)dx
integral of (x^2)/(x^2+x+56)	\int\:\frac{x^{2}}{x^{2}+x+56}dx
parity f(x)=(sin(3x))^{3x}	parity\:f(x)=(\sin(3x))^{3x}
integral of e^{6x}sin(e^{3x})	\int\:e^{6x}\sin(e^{3x})dx
derivative of 2x-x^2	\frac{d}{dx}(2x-x^{2})
integral of e^xsqrt(25+e^x)	\int\:e^{x}\sqrt{25+e^{x}}dx
(dy)/(dx)=(x^2+y^2)/(2xy)	\frac{dy}{dx}=\frac{x^{2}+y^{2}}{2xy}
area y=x,x^2,[0,1]	area\:y=x,x^{2},[0,1]
tangent of y=-(8x)/(x^2+1),(1,-4)	tangent\:y=-\frac{8x}{x^{2}+1},(1,-4)
area x^2+2x+11,-4x+2,x=0	area\:x^{2}+2x+11,-4x+2,x=0
limit as x approaches 6 of \|x-6\|	\lim\:_{x\to\:6}(\left\|x-6\right\|)
y^{''}-3y^'+2y=e^t+e^{2t}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{t}+e^{2t}
derivative of 72x^2	\frac{d}{dx}(72x^{2})
y^{''}+3y^'+2y=x	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=x
tangent of f(x)=5x^2-8x,\at x=1	tangent\:f(x)=5x^{2}-8x,\at\:x=1
limit as x approaches 2 of ax+b	\lim\:_{x\to\:2}(ax+b)
derivative of (2x^2)/(x^2-1)	derivative\:\frac{2x^{2}}{x^{2}-1}
derivative of (e^x/(8x^2))	\frac{d}{dx}(\frac{e^{x}}{8x^{2}})
derivative of (6x-1)/(2x+9)	derivative\:\frac{6x-1}{2x+9}
integral of e^{-z^2}	\int\:e^{-z^{2}}dz
integral of x/(sqrt(x^2+4))	\int\:\frac{x}{\sqrt{x^{2}+4}}dx
limit as x approaches 2 of-1/((x-2)^2)	\lim\:_{x\to\:2}(-\frac{1}{(x-2)^{2}})
derivative of tan(1/2 x)	\frac{d}{dx}(\tan(\frac{1}{2}x))
integral of sin(x+3)	\int\:\sin(x+3)dx
(\partial)/(\partial x)(3x^2+2y^2-4xy+5)	\frac{\partial\:}{\partial\:x}(3x^{2}+2y^{2}-4xy+5)
d/(dt)(t/(1+(1.5574+5.43t^2)^2))	\frac{d}{dt}(\frac{t}{1+(1.5574+5.43t^{2})^{2}})
derivative of (x^3-2x(x^{-4}+x^{-2}))	\frac{d}{dx}((x^{3}-2x)(x^{-4}+x^{-2}))
(\partial)/(\partial x)(3x^2y^3)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{3})
integral of 3-4x	\int\:3-4xdx
derivative of 1+2/x	\frac{d}{dx}(1+\frac{2}{x})
sum from n=1 to infinity of 5(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}5(0.8)^{n-1}
y^{''}+6y^'=0	y^{\prime\:\prime\:}+6y^{\prime\:}=0
integral from 2 to infinity of ye^{-3y}	\int\:_{2}^{\infty\:}ye^{-3y}dy
integral from 0 to 1 of (55)/(4y-1)	\int\:_{0}^{1}\frac{55}{4y-1}dy
integral of 5e^{-3x}(4-e^{-3x})^5	\int\:5e^{-3x}(4-e^{-3x})^{5}dx
derivative of (4x^3+5(x^4-2x))	\frac{d}{dx}((4x^{3}+5)(x^{4}-2x))
limit as x approaches 3 of (\|x\|)/x	\lim\:_{x\to\:3}(\frac{\left\|x\right\|}{x})
integral from 0 to (3pi)/2 of cos^3(41x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(41x)dx
inverse oflaplace s/((s^2+25)(s^2+16))	inverselaplace\:\frac{s}{(s^{2}+25)(s^{2}+16)}
integral of x^2(4x^3-3)^4	\int\:x^{2}(4x^{3}-3)^{4}dx
integral of-6sec^2(x)	\int\:-6\sec^{2}(x)dx
f(x)=2xln(x)+x^2-1	f(x)=2x\ln(x)+x^{2}-1
integral of 5e^xsin^2(x)	\int\:5e^{x}\sin^{2}(x)dx
integral of 9cot^3(x)csc^3(x)	\int\:9\cot^{3}(x)\csc^{3}(x)dx
derivative of 6e^x+4ln(x)	derivative\:6e^{x}+4\ln(x)
y^'-6/x y=(y^4)/(x^{12)}	y^{\prime\:}-\frac{6}{x}y=\frac{y^{4}}{x^{12}}
integral of (4ln(4x^4))/(x^4)	\int\:\frac{4\ln(4x^{4})}{x^{4}}dx
derivative of (4x/(2x^2+1))	\frac{d}{dx}(\frac{4x}{2x^{2}+1})
derivative of (x+2)^2+(10-3x)^2	derivative\:(x+2)^{2}+(10-3x)^{2}
limit as x approaches-1-of (x^2)/(x+1)	\lim\:_{x\to\:-1-}(\frac{x^{2}}{x+1})
integral of x^2-6x-27	\int\:x^{2}-6x-27dx
4x(dy)/(dx)=sqrt(x^2-9)	4x\frac{dy}{dx}=\sqrt{x^{2}-9}
integral from-1 to 1 of ln(ln(x+3))	\int\:_{-1}^{1}\ln(\ln(x+3))dx
(dx)/(dy)=-((4y^2+6xy))/(3y^2+2x)	\frac{dx}{dy}=-\frac{(4y^{2}+6xy)}{3y^{2}+2x}
integral from 0 to 2 of (6x^2-4x+5)	\int\:_{0}^{2}(6x^{2}-4x+5)dx
derivative of y=e^{1/2 x}	derivative\:y=e^{\frac{1}{2}x}
limit as x approaches a of (f(x))/(p(x))	\lim\:_{x\to\:a}(\frac{f(x)}{p(x)})
area y=3-x,y=2x^2,0,1	area\:y=3-x,y=2x^{2},0,1
integral of 1+2y	\int\:1+2ydy
limit as x approaches 1 of sin(-3pix)	\lim\:_{x\to\:1}(\sin(-3πx))
(\partial)/(\partial y)((xy)/(x-y))	\frac{\partial\:}{\partial\:y}(\frac{xy}{x-y})
derivative of x^2-4/(x^3)	\frac{d}{dx}(x^{2}-\frac{4}{x^{3}})
derivative of (8x^2+4x+2/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+4x+2}{\sqrt{x}})
integral from 1 to infinity of x/(e^x)	\int\:_{1}^{\infty\:}\frac{x}{e^{x}}dx

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