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Popular Calculus Problems

integral of-4sin^3(x)	\int\:-4\sin^{3}(x)dx
integral of y^{5/2}	\int\:y^{\frac{5}{2}}dy
derivative of G(r)=sqrt(r)+\sqrt[8]{r}	derivative\:G(r)=\sqrt{r}+\sqrt[8]{r}
integral of xsqrt(x^2)	\int\:x\sqrt{x^{2}}dx
limit as x approaches 2 of 2x^2+5x+3	\lim\:_{x\to\:2}(2x^{2}+5x+3)
integral of 2x(x^2+6)^3	\int\:2x(x^{2}+6)^{3}dx
integral of (\sqrt[10]{x}+\sqrt[11]{x})	\int\:(\sqrt[10]{x}+\sqrt[11]{x})dx
integral of (sin^2(1/t))/(t^2)	\int\:\frac{\sin^{2}(\frac{1}{t})}{t^{2}}dt
sum from n=0 to infinity of (-5x)^n	\sum\:_{n=0}^{\infty\:}(-5x)^{n}
d/(dt)(((t^3)/4-2)+(4/t-3)+cos(t-2))	\frac{d}{dt}((\frac{t^{3}}{4}-2)+(\frac{4}{t}-3)+\cos(t-2))
integral of (-4x^3)/(2x^3+x^2-2x-1)	\int\:\frac{-4x^{3}}{2x^{3}+x^{2}-2x-1}dx
limit as x approaches 1 of 5x^4-5x^2+10	\lim\:_{x\to\:1}(5x^{4}-5x^{2}+10)
f^'(x)=f(x)^4*(4x^2+x)	f^{\prime\:}(x)=f(x)^{4}\cdot\:(4x^{2}+x)
integral of (6x-7)/((2x+1)(4x^2+1))	\int\:\frac{6x-7}{(2x+1)(4x^{2}+1)}dx
laplacetransform s^2+4s+13	laplacetransform\:s^{2}+4s+13
y^'=3x+xy	y^{\prime\:}=3x+xy
derivative of (4x-6^2)	\frac{d}{dx}((4x-6)^{2})
area 9x^2,sqrt(1/9 x)	area\:9x^{2},\sqrt{\frac{1}{9}x}
tangent of f(x)=tan(x+4)	tangent\:f(x)=\tan(x+4)
derivative of (3-xe^x)/(x+e^x)	derivative\:\frac{3-xe^{x}}{x+e^{x}}
derivative of xcos(ln(x))	\frac{d}{dx}(x\cos(\ln(x)))
integral of 2cos(θ)	\int\:2\cos(θ)dθ
tangent of 5e^xcos(x)	tangent\:5e^{x}\cos(x)
derivative of-sin(2/(x+1-e^{x^2}*2x))	\frac{d}{dx}(-\sin(\frac{2}{x+1}-e^{x^{2}}\cdot\:2x))
inverse oflaplace {(3!)/(s^4(s+2)^2)}	inverselaplace\:\left\{\frac{3!}{s^{4}(s+2)^{2}}\right\}
derivative of θtan(θ)	derivative\:θ\tan(θ)
integral of (2x^3-x^2+2x+4)/(x^2+1)	\int\:\frac{2x^{3}-x^{2}+2x+4}{x^{2}+1}dx
integral of e^{20x}	\int\:e^{20x}dx
tangent of f(x)=2x^4,\at x=-2	tangent\:f(x)=2x^{4},\at\:x=-2
integral of cos(x)ln(x)	\int\:\cos(x)\ln(x)dx
integral of (4x-3)/(sqrt(11+10x-x^2))	\int\:\frac{4x-3}{\sqrt{11+10x-x^{2}}}dx
(\partial)/(\partial x)(xcos(y)+y)	\frac{\partial\:}{\partial\:x}(x\cos(y)+y)
derivative of e^{x/8}cos(x/8)	\frac{d}{dx}(e^{\frac{x}{8}}\cos(\frac{x}{8}))
limit as x approaches 0 of sin(x)+1	\lim\:_{x\to\:0}(\sin(x)+1)
integral of (x^2+4)/(3x^2+4x^2-4x)	\int\:\frac{x^{2}+4}{3x^{2}+4x^{2}-4x}dx
implicit x^3+y^3=18xy	implicit\:x^{3}+y^{3}=18xy
integral of pi/(10)sin((pix)/5)	\int\:\frac{π}{10}\sin(\frac{πx}{5})dx
integral of (7-x)	\int\:(7-x)dx
integral from 0 to 1 of (58)/(4y-1)	\int\:_{0}^{1}\frac{58}{4y-1}dy
(dy}{dx}=\frac{xy)/2	\frac{dy}{dx}=\frac{xy}{2}
integral of (2x^3+11x+8)/(x^3+4x^2+4x)	\int\:\frac{2x^{3}+11x+8}{x^{3}+4x^{2}+4x}dx
y^{''''}+17y^{''}+16y=0	y^{\prime\:\prime\:\prime\:\prime\:}+17y^{\prime\:\prime\:}+16y=0
limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2))	\lim\:_{w\to\:0}(\frac{a-\sqrt{w^{2}+a^{2}}}{b-\sqrt{w^{2}+b^{2}}})
tangent of 2x^2+x-3,\at x=-1	tangent\:2x^{2}+x-3,\at\:x=-1
integral of z/(sqrt(1-y^2z^2))	\int\:\frac{z}{\sqrt{1-y^{2}z^{2}}}dy
derivative of y= x/7-7/x	derivative\:y=\frac{x}{7}-\frac{7}{x}
limit as θ approaches 0 of s/d	\lim\:_{θ\to\:0}(\frac{s}{d})
limit as x approaches 0 of xln(x)-x	\lim\:_{x\to\:0}(x\ln(x)-x)
laplacetransform 3+t^5+sin(pit)	laplacetransform\:3+t^{5}+\sin(πt)
(\partial)/(\partial x)(y/(x+z))	\frac{\partial\:}{\partial\:x}(\frac{y}{x+z})
integral from 0 to 4 of 100-10t	\int\:_{0}^{4}100-10tdt
derivative of x^2+3*sqrt(x)	\frac{d}{dx}(x^{2}+3\cdot\:\sqrt{x})
(x^2+4)y^'=xy	(x^{2}+4)y^{\prime\:}=xy
integral of x^3sqrt(x+2)	\int\:x^{3}\sqrt{x+2}dx
integral of xe^{x^{2-1}}	\int\:xe^{x^{2-1}}dx
sqrt(1-7x^2)(dy)/(dx)=x	\sqrt{1-7x^{2}}\frac{dy}{dx}=x
(2xy^4-2xy)dx-(3+3x^2)dy=0	(2xy^{4}-2xy)dx-(3+3x^{2})dy=0
limit as x approaches 1 of (x^2-x)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}-x}{x-1})
(dy}{dx}=\frac{x-2)/x	\frac{dy}{dx}=\frac{x-2}{x}
(\partial)/(\partial y)((2y)/((x+y)^2))	\frac{\partial\:}{\partial\:y}(\frac{2y}{(x+y)^{2}})
derivative of 7e^x	derivative\:7e^{x}
(dx)/(dt)=k(60-x)	\frac{dx}{dt}=k(60-x)
integral of sqrt(x)sqrt(1+x\sqrt{x)}	\int\:\sqrt{x}\sqrt{1+x\sqrt{x}}dx
derivative of f(x)=(2x-1)^2	derivative\:f(x)=(2x-1)^{2}
integral of 1/(1/u+2)	\int\:\frac{1}{\frac{1}{u}+2}du
limit as x approaches 3+of (e^2x)/(x-3)	\lim\:_{x\to\:3+}(\frac{e^{2}x}{x-3})
integral of 1/(x^2+6x)	\int\:\frac{1}{x^{2}+6x}dx
integral of sqrt((x+1))	\int\:\sqrt{(x+1)}dx
d/(dz)(9z^2e^z)	\frac{d}{dz}(9z^{2}e^{z})
slope ofintercept (2,-3),(4,4)	slopeintercept\:(2,-3),(4,4)
(\partial)/(\partial x)(zy^3)	\frac{\partial\:}{\partial\:x}(zy^{3})
derivative of-4*3^x	\frac{d}{dx}(-4\cdot\:3^{x})
derivative of ((x+1(x-2))/(x^2-5x+1))	\frac{d}{dx}(\frac{(x+1)(x-2)}{x^{2}-5x+1})
y^{''}-0.2y^'+0.01y=0,y(0)=11,y^'(0)=b	y^{\prime\:\prime\:}-0.2y^{\prime\:}+0.01y=0,y(0)=11,y^{\prime\:}(0)=b
derivative of e^{xz}	\frac{d}{dx}(e^{xz})
(dy)/(dx)+3y=e^x	\frac{dy}{dx}+3y=e^{x}
derivative of (5-xe^x/(x+e^x))	\frac{d}{dx}(\frac{5-xe^{x}}{x+e^{x}})
taylor 1+e^x	taylor\:1+e^{x}
tangent of f(x)=5x^2,\at x=2	tangent\:f(x)=5x^{2},\at\:x=2
derivative of (1+sin(x)/(xcos(x)))	\frac{d}{dx}(\frac{1+\sin(x)}{x\cos(x)})
limit as x approaches 1 of 3^{(1/x)}	\lim\:_{x\to\:1}(3^{(\frac{1}{x})})
laplacetransform 3sin(3t+2)	laplacetransform\:3\sin(3t+2)
integral of 4x^3e^{2x^4}	\int\:4x^{3}e^{2x^{4}}dx
derivative of ((x^2/(6-x))^5)	\frac{d}{dx}((\frac{x^{2}}{6-x})^{5})
integral from 0 to 1 of x^4-2x^3+x^2	\int\:_{0}^{1}x^{4}-2x^{3}+x^{2}dx
(\partial)/(\partial x)(sqrt(9-2x^2+3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{9-2x^{2}+3y^{2}})
(\partial)/(\partial x)(cos(2x+5y)*5)	\frac{\partial\:}{\partial\:x}(\cos(2x+5y)\cdot\:5)
derivative of-15ln(x)	derivative\:-15\ln(x)
integral from 0 to 1 of e^{-4x^2}	\int\:_{0}^{1}e^{-4x^{2}}dx
y^'=0.0016y(2500-y)	y^{\prime\:}=0.0016y(2500-y)
integral of 1/(x^2+2x+122)	\int\:\frac{1}{x^{2}+2x+122}dx
integral from 0 to infinity of 7/(x^2+4)	\int\:_{0}^{\infty\:}\frac{7}{x^{2}+4}dx
(\partial)/(\partial x)(y^4cos(4x)*4)	\frac{\partial\:}{\partial\:x}(y^{4}\cos(4x)\cdot\:4)
integral of (sqrt(x^2-49))/x	\int\:\frac{\sqrt{x^{2}-49}}{x}dx
area x+y^2=2,x+y=0	area\:x+y^{2}=2,x+y=0
integral from 0 to 3pi of 6x^2sin(1/6 x)	\int\:_{0}^{3π}6x^{2}\sin(\frac{1}{6}x)dx
integral from 0 to 6 of-x^2+6x	\int\:_{0}^{6}-x^{2}+6xdx
derivative of 20x^3	derivative\:20x^{3}
integral from 1 to 6 of 5(ln(x))/(x^2)	\int\:_{1}^{6}5\frac{\ln(x)}{x^{2}}dx
maclaurin f(x)=cos(2x)	maclaurin\:f(x)=\cos(2x)

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