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Popular Calculus Problems

integral of 2x(x^2+2)^6	\int\:2x(x^{2}+2)^{6}dx
(\partial)/(\partial x)(3x^4y^2-2)	\frac{\partial\:}{\partial\:x}(3x^{4}y^{2}-2)
sum from n=1 to infinity of 1/((n)(n+8))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n)(n+8)}
limit as x approaches 4 of y/(sqrt(x))	\lim\:_{x\to\:4}(\frac{y}{\sqrt{x}})
integral of (9x+4)^2	\int\:(9x+4)^{2}dx
integral from 1 to infinity of xe^x	\int\:_{1}^{\infty\:}xe^{x}dx
y^{''}-4y^'+4y=e^x	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{x}
limit as x approaches 2 of 825	\lim\:_{x\to\:2}(825)
derivative of y=e^{-x/2}	derivative\:y=e^{-\frac{x}{2}}
d/(dy)(arctan(y/x))	\frac{d}{dy}(\arctan(\frac{y}{x}))
derivative of 12(x-1/x)^4	derivative\:12(x-\frac{1}{x})^{4}
integral of ((37x+5))/((6x+1)(x-1))	\int\:\frac{(37x+5)}{(6x+1)(x-1)}dx
integral of (1+4x^2)^{1/2}	\int\:(1+4x^{2})^{\frac{1}{2}}dx
2(ln(y))y^'-x^3y=0	2(\ln(y))y^{\prime\:}-x^{3}y=0
integral of (-3)	\int\:(-3)dx
integral of e^{sin(θ)}	\int\:e^{\sin(θ)}dθ
tangent of f(x)=4+3x-2x^2,\at x=2	tangent\:f(x)=4+3x-2x^{2},\at\:x=2
derivative of y=x(x^3+3)^5	derivative\:y=x(x^{3}+3)^{5}
derivative of f(4x^2-2)	derivative\:f(4x^{2}-2)
derivative of f(x)=ln(sqrt(x^2-9))	derivative\:f(x)=\ln(\sqrt{x^{2}-9})
inverse oflaplace sin^2(+t)	inverselaplace\:\sin^{2}(+t)
derivative of sqrt(-x)	\frac{d}{dx}(\sqrt{-x})
(\partial)/(\partial x)(e^{xy}ln(z))	\frac{\partial\:}{\partial\:x}(e^{xy}\ln(z))
integral of t^2cos(t^3)	\int\:t^{2}\cos(t^{3})dt
limit as x approaches 0 of (\|x\|)/x-1	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{x}-1)
derivative of 3/(sqrt(1+x))	\frac{d}{dx}(\frac{3}{\sqrt{1+x}})
y^'-2y=xy^3,y(0)=2sqrt(2)	y^{\prime\:}-2y=xy^{3},y(0)=2\sqrt{2}
(x*y)dx+xdy=0	(x\cdot\:y)dx+xdy=0
limit as x approaches 0 of (sin(1/x))/x	\lim\:_{x\to\:0}(\frac{\sin(\frac{1}{x})}{x})
y^{''}+4y=4sin(2x)	y^{\prime\:\prime\:}+4y=4\sin(2x)
tangent of y=x^2+3,(1,4)	tangent\:y=x^{2}+3,(1,4)
derivative of (x^{{p}(x})/(x^m-a^m))	\frac{d}{dx}(\frac{x^{{p}(x)}}{x^{m}-a^{m}})
(\partial)/(\partial x)(((x+y))/(y^2-x))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{y^{2}-x})
derivative of (1+csc(x^7)/(1-cot(x^7)))	\frac{d}{dx}(\frac{1+\csc(x^{7})}{1-\cot(x^{7})})
derivative of 9/(sqrt(x-6))	derivative\:\frac{9}{\sqrt{x-6}}
integral from 1 to 5 of sqrt(1+(4)^2)	\int\:_{1}^{5}\sqrt{1+(4)^{2}}dx
derivative of 3/(2x)	\frac{d}{dx}(\frac{3}{2x})
limit as x approaches 1 of-3ax+b	\lim\:_{x\to\:1}(-3ax+b)
derivative of (13x^2-26x+26e^x)	\frac{d}{dx}((13x^{2}-26x+26)e^{x})
derivative of e^{x/2}+4x	\frac{d}{dx}(e^{\frac{x}{2}}+4x)
integral from 0 to 4.5 of 100x	\int\:_{0}^{4.5}100xdx
tangent of 4x^2-2x,\at x=-1	tangent\:4x^{2}-2x,\at\:x=-1
derivative of 1/((1+x)^2)	derivative\:\frac{1}{(1+x)^{2}}
xy^'=2x^2+y,y(1)=3	xy^{\prime\:}=2x^{2}+y,y(1)=3
derivative of cos(3ln(x))	\frac{d}{dx}(\cos(3\ln(x)))
derivative of e^x-5x^4	derivative\:e^{x}-5x^{4}
integral of 4/((x+2)^2)	\int\:\frac{4}{(x+2)^{2}}dx
integral of 3xcos(8x)	\int\:3x\cos(8x)dx
sum from n=1 to infinity of 5cos(2/n)	\sum\:_{n=1}^{\infty\:}5\cos(\frac{2}{n})
derivative of 6x^2sin(x)tan(x)	derivative\:6x^{2}\sin(x)\tan(x)
implicit (dy)/(dx),x=y^2	implicit\:\frac{dy}{dx},x=y^{2}
derivative of (400/x)	\frac{d}{dx}(\frac{400}{x})
(dy)/(dx)=(x^2-7)/(15y^2)	\frac{dy}{dx}=\frac{x^{2}-7}{15y^{2}}
derivative of 3x^2+4x-1	\frac{d}{dx}(3x^{2}+4x-1)
integral of (2+2x)/(-x^2-2x+1)	\int\:\frac{2+2x}{-x^{2}-2x+1}dx
inverse oflaplace 1/((s^2+2s+2)s)	inverselaplace\:\frac{1}{(s^{2}+2s+2)s}
(dy)/(dt)=6-1/100 y	\frac{dy}{dt}=6-\frac{1}{100}y
sum from k=1 to infinity of 1/k	\sum\:_{k=1}^{\infty\:}\frac{1}{k}
derivative of (x^2-4^3)	\frac{d}{dx}((x^{2}-4)^{3})
derivative of e^xx+3e^x	\frac{d}{dx}(e^{x}x+3e^{x})
derivative of 2xcos(y)	\frac{d}{dx}(2x\cos(y))
derivative of (12)/(x^3)	derivative\:\frac{12}{x^{3}}
integral of-8	\int\:-8dx
laplacetransform 15t^2	laplacetransform\:15t^{2}
derivative of-4csc^2(x)+4sec^2(x)	derivative\:-4\csc^{2}(x)+4\sec^{2}(x)
derivative of y=(x^2+x+1)^{100}	derivative\:y=(x^{2}+x+1)^{100}
(\partial)/(\partial x)(15xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(15xye^{-x^{2}-y^{2}})
integral of x/((16+x^2)^{3/2)}	\int\:\frac{x}{(16+x^{2})^{\frac{3}{2}}}dx
parity y=ln(sqrt((1+sin(x))/(1-sin(x))))	parity\:y=\ln(\sqrt{\frac{1+\sin(x)}{1-\sin(x)}})
derivative of x(3x+1^5)	\frac{d}{dx}(x(3x+1)^{5})
limit as x approaches 1 of (sin(x-1))/x	\lim\:_{x\to\:1}(\frac{\sin(x-1)}{x})
integral of (ln(2x))/(3x)	\int\:\frac{\ln(2x)}{3x}dx
tangent of f(x)=3sin(x),\at x=-pi/4	tangent\:f(x)=3\sin(x),\at\:x=-\frac{π}{4}
derivative of y=80(1-e^{-0.041x})	derivative\:y=80(1-e^{-0.041x})
(\partial)/(\partial x)(y(x^2+y)^6)	\frac{\partial\:}{\partial\:x}(y(x^{2}+y)^{6})
limit as x approaches-1 of sqrt(x+5)	\lim\:_{x\to\:-1}(\sqrt{x+5})
(\partial)/(\partial x)(4x+2y)	\frac{\partial\:}{\partial\:x}(4x+2y)
derivative of 2/(5x-1)	\frac{d}{dx}(\frac{2}{5x-1})
inverse oflaplace 4/s	inverselaplace\:\frac{4}{s}
integral of (x+5)^9	\int\:(x+5)^{9}dx
integral of x^2sqrt(5x+4)	\int\:x^{2}\sqrt{5x+4}dx
area f(x)=x^3-6x^2+8,g(x)=x^2-4x	area\:f(x)=x^{3}-6x^{2}+8,g(x)=x^{2}-4x
(dy)/(dx)=(x-8)e^{-2y}	\frac{dy}{dx}=(x-8)e^{-2y}
derivative of f(x)=2x+6	derivative\:f(x)=2x+6
implicit 2x^2+xy+y^2=4	implicit\:2x^{2}+xy+y^{2}=4
derivative of f(x)=(x^2-4x+3)/(x+1)	derivative\:f(x)=\frac{x^{2}-4x+3}{x+1}
integral of 1/(1-tan(6x))	\int\:\frac{1}{1-\tan(6x)}dx
limit as x approaches 1 of x^3-2x^2-7x-6	\lim\:_{x\to\:1}(x^{3}-2x^{2}-7x-6)
limit as x approaches infinity of (-1)^x	\lim\:_{x\to\:\infty\:}((-1)^{x})
integral of 1/(4tsqrt(t^2-16))	\int\:\frac{1}{4t\sqrt{t^{2}-16}}dt
y^'=2x^2	y^{\prime\:}=2x^{2}
derivative of e^{2x}+xe^{2x}+cos(2x)	derivative\:e^{2x}+xe^{2x}+\cos(2x)
(\partial)/(\partial x)(ln(ycos(x)))	\frac{\partial\:}{\partial\:x}(\ln(y\cos(x)))
normal of y=e^x,\at x=ln(2)	normal\:y=e^{x},\at\:x=\ln(2)
integral of x(2x+5)^{20}	\int\:x(2x+5)^{20}dx
(\partial)/(\partial x)(7e^xsin(y))	\frac{\partial\:}{\partial\:x}(7e^{x}\sin(y))
limit as x approaches 2 of sqrt(7x-4)	\lim\:_{x\to\:2}(\sqrt{7x-4})
limit as x approaches 2 of (x^3+1)/(x+1)	\lim\:_{x\to\:2}(\frac{x^{3}+1}{x+1})
limit as x approaches 9 of (e^{5x}-1)/x	\lim\:_{x\to\:9}(\frac{e^{5x}-1}{x})
integral of (sqrt(x)+1/(sqrt(x)))^2	\int\:(\sqrt{x}+\frac{1}{\sqrt{x}})^{2}dx

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