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Popular Calculus Problems

integral of (x^2-3)/((x+1)^3)	\int\:\frac{x^{2}-3}{(x+1)^{3}}dx
y^{''}-6y^'+25y=3t-2cos(5t)	y^{\prime\:\prime\:}-6y^{\prime\:}+25y=3t-2\cos(5t)
integral of (6e^{7x})	\int\:(6e^{7x})dx
integral of (sin(a)x)/(sqrt(c+cos(a)x))	\int\:\frac{\sin(a)x}{\sqrt{c+\cos(a)x}}dx
integral of 1/7 x^{-6/7}	\int\:\frac{1}{7}x^{-\frac{6}{7}}dx
tangent of y^2+xy+x^2=1,(0,1)	tangent\:y^{2}+xy+x^{2}=1,(0,1)
x(dy)/(dx)=x^{-3}-2y	x\frac{dy}{dx}=x^{-3}-2y
integral from 1 to 4 of 3/x	\int\:_{1}^{4}\frac{3}{x}dx
inverse oflaplace 3/(2s^2+3s+1)	inverselaplace\:\frac{3}{2s^{2}+3s+1}
(dy)/(dx)=sqrt(2y)e^{x+7}	\frac{dy}{dx}=\sqrt{2y}e^{x+7}
limit as x approaches 1-of 3	\lim\:_{x\to\:1-}(3)
derivative of (x^2)/(x+1)	derivative\:\frac{x^{2}}{x+1}
d/(dy)(cos(x)sin(y))	\frac{d}{dy}(\cos(x)\sin(y))
derivative of 3/(sin(x)+cos(x))	derivative\:\frac{3}{\sin(x)+\cos(x)}
sum from i=1 to infinity of i^4	\sum\:_{i=1}^{\infty\:}i^{4}
(\partial)/(\partial x)(3x^4+8x^3)	\frac{\partial\:}{\partial\:x}(3x^{4}+8x^{3})
d/(d{z)}((1-{y}){z})	\frac{d}{d{z}}((1-{y}){z})
(dy)/(dx)=3y	\frac{dy}{dx}=3y
(\partial)/(\partial y)(5x^2)	\frac{\partial\:}{\partial\:y}(5x^{2})
integral of (128)/(w^2sqrt(64-w^2))	\int\:\frac{128}{w^{2}\sqrt{64-w^{2}}}dw
(\partial)/(\partial x)(2^{40})	\frac{\partial\:}{\partial\:x}(2^{40})
integral of 1/(sin(x)cos(x))	\int\:\frac{1}{\sin(x)\cos(x)}dx
limit as x approaches-2 of (z+2)/(x^2+4)	\lim\:_{x\to\:-2}(\frac{z+2}{x^{2}+4})
integral of 3sec^2(x)tan(x)	\int\:3\sec^{2}(x)\tan(x)dx
limit as x approaches 3 of In(x^2-9)	\lim\:_{x\to\:3}(In(x^{2}-9))
integral of e^{ax}sin(b)x	\int\:e^{ax}\sin(b)xdx
(\partial)/(\partial y)(yarcsin(xy))	\frac{\partial\:}{\partial\:y}(y\arcsin(xy))
derivative of f(x)=3-x+x^2	derivative\:f(x)=3-x+x^{2}
tangent of x/(sqrt(x+5))	tangent\:\frac{x}{\sqrt{x+5}}
derivative of-cos(x+sin(x))	\frac{d}{dx}(-\cos(x)+\sin(x))
derivative of f(x)=(3x^2+1)^4	derivative\:f(x)=(3x^{2}+1)^{4}
tangent of 3+5x^2-2x^3	tangent\:3+5x^{2}-2x^{3}
integral of (sqrt(x^2-4))/(x^2)	\int\:\frac{\sqrt{x^{2}-4}}{x^{2}}dx
integral of (3/x+x)	\int\:(\frac{3}{x}+x)dx
area y=2sqrt(x),y=2x^3	area\:y=2\sqrt{x},y=2x^{3}
integral from 0 to 13/12 of 68/3 x	\int\:_{0}^{\frac{13}{12}}\frac{68}{3}xdx
derivative of y=2x^2-9x+10	derivative\:y=2x^{2}-9x+10
derivative of 17.5(x+1^{0.75})	\frac{d}{dx}(17.5(x+1)^{0.75})
sum from k=1 to infinity of 8(1/5)^k	\sum\:_{k=1}^{\infty\:}8(\frac{1}{5})^{k}
tangent of sin(x)cos(x)	tangent\:\sin(x)\cos(x)
tangent of (8x)/((x^2+1))	tangent\:\frac{8x}{(x^{2}+1)}
limit as x approaches 0-of ln(x)	\lim\:_{x\to\:0-}(\ln(x))
integral of 8/((4-t)^8)	\int\:\frac{8}{(4-t)^{8}}dt
tangent of y=8+4x^2-2x^3,(2,8)	tangent\:y=8+4x^{2}-2x^{3},(2,8)
limit as x approaches 2 of x^2+3x-4	\lim\:_{x\to\:2}(x^{2}+3x-4)
integral of x/(x^4+7)	\int\:\frac{x}{x^{4}+7}dx
integral of (x^2+y^2+z^2)	\int\:(x^{2}+y^{2}+z^{2})dx
integral of (3+6x)/(1+x^2)	\int\:\frac{3+6x}{1+x^{2}}dx
derivative of x*ln(x+1)	\frac{d}{dx}(x\cdot\:\ln(x+1))
derivative of 4/(sqrt(1+x))	\frac{d}{dx}(\frac{4}{\sqrt{1+x}})
integral of 8/(x(ln(x)+1)^{3/2)}	\int\:\frac{8}{x(\ln(x)+1)^{\frac{3}{2}}}dx
derivative of 3x-4	derivative\:3x-4
integral of sin(t-s)	\int\:\sin(t-s)ds
tangent of 5/(4-x),\at x=-3	tangent\:\frac{5}{4-x},\at\:x=-3
integral of 1/(sqrt(-x^2+10x))	\int\:\frac{1}{\sqrt{-x^{2}+10x}}dx
integral of x^7*sin(x^4)	\int\:x^{7}\cdot\:\sin(x^{4})dx
f(x)=cos(x^2)	f(x)=\cos(x^{2})
sum from n=1 to infinity of n(4/3)^n	\sum\:_{n=1}^{\infty\:}n(\frac{4}{3})^{n}
tangent of f(x)=2x-3x^2,\at x=-1	tangent\:f(x)=2x-3x^{2},\at\:x=-1
(dy)/(dt)=y+2t	\frac{dy}{dt}=y+2t
derivative of-19.6t+2	derivative\:-19.6t+2
f(x)=sin(x^4)	f(x)=\sin(x^{4})
integral of (9x^2-4x+2)	\int\:(9x^{2}-4x+2)dx
inverse oflaplace 4/((s+1)(s^2+4s+8))	inverselaplace\:\frac{4}{(s+1)(s^{2}+4s+8)}
limit as x approaches-2 of (x-3)/(x+5)	\lim\:_{x\to\:-2}(\frac{x-3}{x+5})
(\partial)/(\partial y)(-xsin(y))	\frac{\partial\:}{\partial\:y}(-x\sin(y))
y^'=(t+y)^2-1,y(1)=6	y^{\prime\:}=(t+y)^{2}-1,y(1)=6
derivative of 4x+2x^2sin(1/x)	\frac{d}{dx}(4x+2x^{2}\sin(\frac{1}{x}))
integral of sin(x-nx)	\int\:\sin(x-nx)dx
derivative of (sqrt(5x-1)+2^6)	\frac{d}{dx}((\sqrt{5x-1}+2)^{6})
integral from-2 to 3 of x^2+4	\int\:_{-2}^{3}x^{2}+4dx
integral of (e 1/x)/(x^2)	\int\:\frac{e\frac{1}{x}}{x^{2}}dx
y^'+2xy=0	y^{\prime\:}+2xy=0
integral of sec^4(1)	\int\:\sec^{4}(1)dx
tangent of f(x)= 4/(1+x^2)	tangent\:f(x)=\frac{4}{1+x^{2}}
xy^2(dy)/(dx)=y^3-x^3	xy^{2}\frac{dy}{dx}=y^{3}-x^{3}
laplacetransform cos(-2t)	laplacetransform\:\cos(-2t)
integral of 23x	\int\:23xdx
y^'= y/t	y^{\prime\:}=\frac{y}{t}
y^{''}+4y=16sin(2t)	y^{\prime\:\prime\:}+4y=16\sin(2t)
tangent of f(x)=9+4x^2-2x^3,\at x=a	tangent\:f(x)=9+4x^{2}-2x^{3},\at\:x=a
tangent of y=sqrt(3x+4),(7,5)	tangent\:y=\sqrt{3x+4},(7,5)
yy^'=-x	yy^{\prime\:}=-x
limit as x approaches 1 of \|e^{x-1}-1\|	\lim\:_{x\to\:1}(\left\|e^{x-1}-1\right\|)
derivative of f(x)=(x^2)/((4+x))	derivative\:f(x)=\frac{x^{2}}{(4+x)}
derivative of f(x)=-cot(x)csc(x)	derivative\:f(x)=-\cot(x)\csc(x)
derivative of \sqrt[3]{x+2}	derivative\:\sqrt[3]{x+2}
derivative of f(x)=x(ln(x))-x	derivative\:f(x)=x(\ln(x))-x
derivative of f(x)=sqrt((x^2-3x)/(2x+1))	derivative\:f(x)=\sqrt{\frac{x^{2}-3x}{2x+1}}
integral of ((7x^2+x+7))/((x^2+1)^2)	\int\:\frac{(7x^{2}+x+7)}{(x^{2}+1)^{2}}dx
integral of (x^3+1)/(x^2-4)	\int\:\frac{x^{3}+1}{x^{2}-4}dx
integral from 0 to 4 of e^{-x}	\int\:_{0}^{4}e^{-x}dx
sum from n=1 to infinity of (1/4)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{4})^{n}
derivative of f(x)=x^4+5x	derivative\:f(x)=x^{4}+5x
derivative of ln(1+x-x)	\frac{d}{dx}(\ln(1+x)-x)
integral of 8we^{7w}	\int\:8we^{7w}dw
integral of (8-128x)/(sqrt(1-64x^2))	\int\:\frac{8-128x}{\sqrt{1-64x^{2}}}dx
integral of 4/(x^2-4)	\int\:\frac{4}{x^{2}-4}dx
integral of 12xe^{-x^2}	\int\:12xe^{-x^{2}}dx
integral of 7/(x^2+25)	\int\:\frac{7}{x^{2}+25}dx

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