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Popular Calculus Problems

integral of cos(2x)cos(4x)	\int\:\cos(2x)\cos(4x)dx
derivative of {f}(h,x{g}(h,x)h)	\frac{d}{dx}({f}(h,x)\cdot\:{g}(h,x)\cdot\:h)
derivative of 1/(sqrt(5x))	\frac{d}{dx}(\frac{1}{\sqrt{5x}})
integral of (sin(x)sqrt(x))/(sqrt(x))	\int\:\frac{\sin(x)\sqrt{x}}{\sqrt{x}}dx
derivative of (3x^2+3)(2x^2+1)	derivative\:(3x^{2}+3)(2x^{2}+1)
integral of-y/(x^2+y^2)	\int\:-\frac{y}{x^{2}+y^{2}}dx
limit as x approaches 2 of x^3-8	\lim\:_{x\to\:2}(x^{3}-8)
y^'(t)=(y+1)(y-1),y(0)=3	y^{\prime\:}(t)=(y+1)(y-1),y(0)=3
implicit (dy)/(dx),(2x+3)^4=3y^4	implicit\:\frac{dy}{dx},(2x+3)^{4}=3y^{4}
derivative of f(x)=5x^2-2x+5	derivative\:f(x)=5x^{2}-2x+5
taylor cos(x^2)	taylor\:\cos(x^{2})
(\partial)/(\partial u)(u^2+v^2-4)	\frac{\partial\:}{\partial\:u}(u^{2}+v^{2}-4)
integral of x*(sqrt(x^2-3))	\int\:x\cdot\:(\sqrt{x^{2}-3})dx
derivative of y=xsin(1/x)	derivative\:y=x\sin(\frac{1}{x})
derivative of 3x^2(x^3+1)^7	derivative\:3x^{2}(x^{3}+1)^{7}
limit as x approaches 0 of (sin^2(4x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(4x)}{x})
limit as x approaches 0+of-1/(sin(2x))	\lim\:_{x\to\:0+}(-\frac{1}{\sin(2x)})
laplacetransform 4(t+3)	laplacetransform\:4(t+3)
derivative of yx^{y-1}	\frac{d}{dx}(yx^{y-1})
integral of (2sin(x)cos(x))/(1+tan(x))	\int\:\frac{2\sin(x)\cos(x)}{1+\tan(x)}dx
y^{''}+y^'=1	y^{\prime\:\prime\:}+y^{\prime\:}=1
integral from 0 to 1 of (e^{1/x})/(x^3)	\int\:_{0}^{1}\frac{e^{\frac{1}{x}}}{x^{3}}dx
slope of (0,2.5),(0.833,0)	slope\:(0,2.5),(0.833,0)
tangent of f(x)=2x^3-2x,\at x=-1	tangent\:f(x)=2x^{3}-2x,\at\:x=-1
(\partial)/(\partial y)(sin(x+2y))	\frac{\partial\:}{\partial\:y}(\sin(x+2y))
integral from 0 to pi of 2pixsin(x)	\int\:_{0}^{π}2πx\sin(x)dx
(\partial)/(\partial x)((xy)^5)	\frac{\partial\:}{\partial\:x}((xy)^{5})
derivative of x^2*In(x)	\frac{d}{dx}(x^{2}\cdot\:In(x))
tangent of f(x)=(1+2x)(6-5x),\at x=1	tangent\:f(x)=(1+2x)(6-5x),\at\:x=1
(\partial)/(\partial x)(2ln(xy))	\frac{\partial\:}{\partial\:x}(2\ln(xy))
integral of x^2arcsin(x)	\int\:x^{2}\arcsin(x)dx
integral of ((ln(x))^{28})/x	\int\:\frac{(\ln(x))^{28}}{x}dx
derivative of arcsin(3x+1)	\frac{d}{dx}(\arcsin(3x+1))
(\partial)/(\partial z)(xyz^2tan(yt))	\frac{\partial\:}{\partial\:z}(xyz^{2}\tan(yt))
maclaurin sin^2(x)	maclaurin\:\sin^{2}(x)
derivative of f(x)=x+3+4/x	derivative\:f(x)=x+3+\frac{4}{x}
d/(dt)(-1)	\frac{d}{dt}(-1)
integral of (26)/(x(x^2+4)^2)	\int\:\frac{26}{x(x^{2}+4)^{2}}dx
inverse oflaplace 1/((s+1)^2(s^2+4))	inverselaplace\:\frac{1}{(s+1)^{2}(s^{2}+4)}
integral of 1/(9x^2-144)	\int\:\frac{1}{9x^{2}-144}dx
area y=sqrt(x+2),y= 1/(x+1),x=2	area\:y=\sqrt{x+2},y=\frac{1}{x+1},x=2
derivative of 2cot(x)	\frac{d}{dx}(2\cot(x))
(\partial)/(\partial x)(2x^2-2xy^2)	\frac{\partial\:}{\partial\:x}(2x^{2}-2xy^{2})
integral of sqrt((x+3)/(x-1))	\int\:\sqrt{\frac{x+3}{x-1}}dx
derivative of arcsin(x/pi)	\frac{d}{dx}(\arcsin(\frac{x}{π}))
integral from 0 to 4 of x^2+1	\int\:_{0}^{4}x^{2}+1dx
inverse oflaplace (1+s2)/((1+s3)^2)	inverselaplace\:\frac{1+s\cdot\:2}{(1+s\cdot\:3)^{2}}
derivative of f(x)=x^2sin(1/x)	derivative\:f(x)=x^{2}\sin(\frac{1}{x})
d/(dy)(y/(x^2+y^2))	\frac{d}{dy}(\frac{y}{x^{2}+y^{2}})
integral of (3x^2)/((x^3+1)^5)	\int\:\frac{3x^{2}}{(x^{3}+1)^{5}}dx
laplacetransform x*e^{-Ax}	laplacetransform\:x\cdot\:e^{-Ax}
derivative of x/((2x-1^6))	\frac{d}{dx}(\frac{x}{(2x-1)^{6}})
integral of (4x+3)^3	\int\:(4x+3)^{3}dx
f(x)=e^{x^2}*2x	f(x)=e^{x^{2}}\cdot\:2x
integral of 5x^3sqrt(1-x^2)	\int\:5x^{3}\sqrt{1-x^{2}}dx
(\partial)/(\partial x)(2x^2-4xy+xyz)	\frac{\partial\:}{\partial\:x}(2x^{2}-4xy+xyz)
(\partial)/(\partial x)(((x(y+3)))/(x^2+y))	\frac{\partial\:}{\partial\:x}(\frac{(x(y+3))}{x^{2}+y})
x^4e^y+(x+1)y(dy)/(dx)=0	x^{4}e^{y}+(x+1)y\frac{dy}{dx}=0
derivative of f(x)=(1+cos^2(x))^6	derivative\:f(x)=(1+\cos^{2}(x))^{6}
derivative of arcsin(sqrt(x))	derivative\:\arcsin(\sqrt{x})
integral from 5 to 10 of ax-10b	\int\:_{5}^{10}ax-10bdx
tangent of f(x)=(12)/x ,\at x=-2	tangent\:f(x)=\frac{12}{x},\at\:x=-2
d/(dz)(0)	\frac{d}{dz}(0)
limit as x approaches 0 of 1/(x^{1/2)}	\lim\:_{x\to\:0}(\frac{1}{x^{\frac{1}{2}}})
integral of (ye^x+sin(y))	\int\:(ye^{x}+\sin(y))dx
y^{''}+2y+8=0	y^{\prime\:\prime\:}+2y+8=0
derivative of ln(sec(ln(x)))	derivative\:\ln(\sec(\ln(x)))
integral of-1/(u^2)	\int\:-\frac{1}{u^{2}}du
(\partial)/(\partial y)((-y^2)/((x-y)^2))	\frac{\partial\:}{\partial\:y}(\frac{-y^{2}}{(x-y)^{2}})
integral of (sqrt(x))^2	\int\:(\sqrt{x})^{2}dx
integral of 1/(xln(x)(ln(ln(x)))^2)	\int\:\frac{1}{x\ln(x)(\ln(\ln(x)))^{2}}dx
(1+x^2+y^2+x^2y^2)dy=(1+y^2)dx	(1+x^{2}+y^{2}+x^{2}y^{2})dy=(1+y^{2})dx
integral of (100)/(100-y)	\int\:\frac{100}{100-y}dy
y^{'''}+4*y^'=3x-1	y^{\prime\:\prime\:\prime\:}+4\cdot\:y^{\prime\:}=3x-1
limit as x approaches 1 of e^{4x^5-4x}	\lim\:_{x\to\:1}(e^{4x^{5}-4x})
integral of (2x-1)^2	\int\:(2x-1)^{2}dx
(\partial)/(\partial x)(x^2y^3+2x^4y)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+2x^{4}y)
limit as x approaches infinity of 2/x-6	\lim\:_{x\to\:\infty\:}(\frac{2}{x}-6)
derivative of 3x^4-5x^2+1	\frac{d}{dx}(3x^{4}-5x^{2}+1)
d/(dy)((2x)/(x^2+y^2))	\frac{d}{dy}(\frac{2x}{x^{2}+y^{2}})
derivative of (4-x^2^3)	\frac{d}{dx}((4-x^{2})^{3})
integral of (sin(2/x))/(x^2)	\int\:\frac{\sin(\frac{2}{x})}{x^{2}}dx
derivative of 5/3 x^2y^{-2}	\frac{d}{dx}(\frac{5}{3}x^{2}y^{-2})
integral of 2/(sqrt(x^2+9))	\int\:\frac{2}{\sqrt{x^{2}+9}}dx
sum from n=0 to infinity of n/(1+n^2)	\sum\:_{n=0}^{\infty\:}\frac{n}{1+n^{2}}
tangent of f(x)= 2/(x^2),(7, 2/49)	tangent\:f(x)=\frac{2}{x^{2}},(7,\frac{2}{49})
derivative of ln(sqrt(3x^2+1))	\frac{d}{dx}(\ln(\sqrt{3x^{2}+1}))
d/(dy)(y/(y+b/y))	\frac{d}{dy}(\frac{y}{y+\frac{b}{y}})
integral of 2x(x^2+1)^{23}	\int\:2x(x^{2}+1)^{23}dx
sum from n=1 to infinity of-1/(3(3n+2))	\sum\:_{n=1}^{\infty\:}-\frac{1}{3(3n+2)}
integral of 1/(yln(y))	\int\:\frac{1}{y\ln(y)}dy
(\partial)/(\partial v)(u+2v)	\frac{\partial\:}{\partial\:v}(u+2v)
integral from 1 to 2 of (v^6+4v^8)/(v^5)	\int\:_{1}^{2}\frac{v^{6}+4v^{8}}{v^{5}}dv
y^{''}+4y^'-16y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-16y=0
(\partial)/(\partial y)(3x^2(1+ln(y)))	\frac{\partial\:}{\partial\:y}(3x^{2}(1+\ln(y)))
limit as x approaches 0 of (2+x-2)/x	\lim\:_{x\to\:0}(\frac{2+x-2}{x})
(\partial)/(\partial x)(sqrt(13-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{13-x^{2}-y^{2}})
integral of 9sin^2(xco)s^3x	\int\:9\sin^{2}(xco)s^{3}xdx
area 9x=y^2+27,3<= x<= 7	area\:9x=y^{2}+27,3\le\:x\le\:7
integral from 0 to 1 of x^2e^{3x}	\int\:_{0}^{1}x^{2}e^{3x}dx

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