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Popular Calculus Problems

derivative of f(x)=(x+2)(2x^2-2)	derivative\:f(x)=(x+2)\cdot\:(2\cdot\:x^{2}-2)
integral of-3sec(x)tan(x)-3csc(x)cot(x)	\int\:-3\sec(x)\tan(x)-3\csc(x)\cot(x)dx
integral of 1/(6x)	\int\:\frac{1}{6x}dx
(t-sin(t))^'	(t-\sin(t))^{\prime\:}
derivative of log_{2}(x^2)	\frac{d}{dx}(\log_{2}(x^{2}))
area x^2,2,5	area\:x^{2},2,5
sum from n=1 to infinity of 4/(nln(8n))	\sum\:_{n=1}^{\infty\:}\frac{4}{n\ln(8n)}
derivative of ln(x^4)	derivative\:\ln(x^{4})
f(x)=(sec(x))/(1+tan(x))	f(x)=\frac{\sec(x)}{1+\tan(x)}
integral from 0 to 1 of (u+4)(u-5)	\int\:_{0}^{1}(u+4)(u-5)du
area x=1,x+y=6	area\:x=1,x+y=6
taylor (e^x-(1+x))/(7x^2)	taylor\:\frac{e^{x}-(1+x)}{7x^{2}}
(\partial)/(\partial x)(e^{-x}*cos(y))	\frac{\partial\:}{\partial\:x}(e^{-x}\cdot\:\cos(y))
integral of x^{-1}ln(x)	\int\:x^{-1}\ln(x)dx
limit as x approaches-3 of (x+3)/(x+3)	\lim\:_{x\to\:-3}(\frac{x+3}{x+3})
derivative of f(x)=sqrt(17x)	derivative\:f(x)=\sqrt{17x}
integral of (sqrt(x^2+9))/(x^2)	\int\:\frac{\sqrt{x^{2}+9}}{x^{2}}dx
derivative of (8t)/(8+sqrt(t))	derivative\:\frac{8t}{8+\sqrt{t}}
integral of (3x^2)/2	\int\:\frac{3x^{2}}{2}dx
(\partial)/(\partial x)(3x^{1/3}y^{2/3})	\frac{\partial\:}{\partial\:x}(3x^{\frac{1}{3}}y^{\frac{2}{3}})
limit as x approaches 0 of 7/(1+e^{1/x)}	\lim\:_{x\to\:0}(\frac{7}{1+e^{\frac{1}{x}}})
integral of 1/(7xlog_{3)(x)}	\int\:\frac{1}{7x\log_{3}(x)}dx
limit as x approaches 2 of 2x^2+4x-5	\lim\:_{x\to\:2}(2x^{2}+4x-5)
integral from 0 to 4 of 400-20t	\int\:_{0}^{4}400-20tdt
integral of ((e^x)/(e^x+1))	\int\:(\frac{e^{x}}{e^{x}+1})dx
(\partial)/(\partial x)(ycos(xlog_{e}(y)))	\frac{\partial\:}{\partial\:x}(y\cos(x\log_{e}(y)))
limit as x approaches infinity of 2/0	\lim\:_{x\to\:\infty\:}(\frac{2}{0})
(dy)/(dt)=-3(y-5)	\frac{dy}{dt}=-3(y-5)
limit as x approaches infinity of ((\frac{x+1)/(x^3+2))}{(x/(x^3))}	\lim\:_{x\to\:\infty\:}(\frac{(\frac{x+1}{x^{3}+2})}{(\frac{x}{x^{3}})})
limit as x approaches 5+of 8/(x-5)	\lim\:_{x\to\:5+}(\frac{8}{x-5})
integral of sin(ln(2x))	\int\:\sin(\ln(2x))dx
derivative of 2sin(2x-2cos(2x)-1/5 e^x)	\frac{d}{dx}(2\sin(2x)-2\cos(2x)-\frac{1}{5}e^{x})
derivative of (x-5^2)	\frac{d}{dx}((x-5)^{2})
sum from n=0 to infinity of (-1)^n*n	\sum\:_{n=0}^{\infty\:}(-1)^{n}\cdot\:n
y=-80+208	y=-80+208
(\partial)/(\partial y)(tan(x)y^{2.5})	\frac{\partial\:}{\partial\:y}(\tan(x)y^{2.5})
derivative of (x^3+2xe^{sin(x)})	\frac{d}{dx}((x^{3}+2x)e^{\sin(x)})
derivative of f(x)=-1/3 t^3+64t+3000	derivative\:f(x)=-\frac{1}{3}t^{3}+64t+3000
y^'=(1-y^2)/y	y^{\prime\:}=\frac{1-y^{2}}{y}
integral of ((x-7))/(x^2-18x+82)	\int\:\frac{(x-7)}{x^{2}-18x+82}dx
derivative of sqrt(x^2+25)	derivative\:\sqrt{x^{2}+25}
derivative of (1+e^x)/(1-e^x)	derivative\:\frac{1+e^{x}}{1-e^{x}}
derivative of ((x+5/(x-5))^5)	\frac{d}{dx}((\frac{x+5}{x-5})^{5})
integral of sin(3x)tan(3x)	\int\:\sin(3x)\tan(3x)dx
sum from n=2 to infinity of ne^{-2n}	\sum\:_{n=2}^{\infty\:}ne^{-2n}
derivative of f(x)=sin(2x^2)	derivative\:f(x)=\sin(2x^{2})
integral from 0 to 2 of 2pix(1+(x^2)/2)	\int\:_{0}^{2}2πx(1+\frac{x^{2}}{2})dx
limit as x approaches 1 of x^2+8x-2	\lim\:_{x\to\:1}(x^{2}+8x-2)
derivative of 2x^2cos(2x)	\frac{d}{dx}(2x^{2}\cos(2x))
tangent of y=2cos(x),\at x= pi/3	tangent\:y=2\cos(x),\at\:x=\frac{π}{3}
tangent of y^2+5x=x^2y-5,(3,5)	tangent\:y^{2}+5x=x^{2}y-5,(3,5)
area x=y^2,x=3-2y^2	area\:x=y^{2},x=3-2y^{2}
derivative of x^4sqrt(x)	\frac{d}{dx}(x^{4}\sqrt{x})
integral of (3x)/(sqrt(x^4+6x^2+5))	\int\:\frac{3x}{\sqrt{x^{4}+6x^{2}+5}}dx
limit as x approaches 0+of (1+ax)^{b/x}	\lim\:_{x\to\:0+}((1+ax)^{\frac{b}{x}})
derivative of (x^3-1/2)	\frac{d}{dx}(\frac{x^{3}-1}{2})
(\partial)/(\partial x)(2xcos(x))	\frac{\partial\:}{\partial\:x}(2x\cos(x))
x^2y^'-xy+3y^2=0	x^{2}y^{\prime\:}-xy+3y^{2}=0
(d^4)/(dx^4)(x^x)	\frac{d^{4}}{dx^{4}}(x^{x})
integral of (sqrt(4-3x)-sqrt(x))	\int\:(\sqrt{4-3x}-\sqrt{x})dx
derivative of x^3-3x^2-9x+11	\frac{d}{dx}(x^{3}-3x^{2}-9x+11)
integral of (6e^{-6x})/(2-e^{-6x)}	\int\:\frac{6e^{-6x}}{2-e^{-6x}}dx
integral of e^{1/y}	\int\:e^{\frac{1}{y}}dy
derivative of 4sqrt(x)-2x	derivative\:4\sqrt{x}-2x
derivative of log_{2}(e^{-x}cos(pix))	derivative\:\log_{2}(e^{-x}\cos(πx))
limit as x approaches infinity of r^x	\lim\:_{x\to\:\infty\:}(r^{x})
integral of ((x^2+1))/(\sqrt[3]{x)}	\int\:\frac{(x^{2}+1)}{\sqrt[3]{x}}dx
limit as x approaches 0+of 1-1/x	\lim\:_{x\to\:0+}(1-\frac{1}{x})
implicit (dy)/(dx),x^3-3x^2y+2xy^2=12	implicit\:\frac{dy}{dx},x^{3}-3x^{2}y+2xy^{2}=12
derivative of x^2(1-6x)	derivative\:x^{2}(1-6x)
area x/((x^2+5x+6)),0,1	area\:\frac{x}{(x^{2}+5x+6)},0,1
integral of e^{-θx}	\int\:e^{-θx}dx
d/(d{x)}({x}+{y}-{z})	\frac{d}{d{x}}({x}+{y}-{z})
derivative of f(x)=e^{5x}	derivative\:f(x)=e^{5x}
integral of 2x^3sqrt(1+x^2)	\int\:2x^{3}\sqrt{1+x^{2}}dx
(dy)/(dt)= 1/((y+2)^2),y(0)=1	\frac{dy}{dt}=\frac{1}{(y+2)^{2}},y(0)=1
tangent of y= 1/(1+x^2),(1, 1/2)	tangent\:y=\frac{1}{1+x^{2}},(1,\frac{1}{2})
derivative of x^5e^{-3ln(x})	\frac{d}{dx}(x^{5}e^{-3\ln(x)})
derivative of (x^2-5x^3)	\frac{d}{dx}((x^{2}-5x)^{3})
integral of (2x+1)/((x+1)(x-2))	\int\:\frac{2x+1}{(x+1)(x-2)}dx
(dy)/(dx)+5(tan(5x))y=4cos(5x)	\frac{dy}{dx}+5(\tan(5x))y=4\cos(5x)
limit as x approaches 0+of (x^2)/4-2/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{4}-\frac{2}{x})
derivative of sqrt(x(x+4))	\frac{d}{dx}(\sqrt{x(x+4)})
integral of sec^2(5xta)n^35x	\int\:\sec^{2}(5xta)n^{3}5xdx
integral of cos(x)cos(5x)	\int\:\cos(x)\cos(5x)dx
area f(x)=x^2,(1,5),5	area\:f(x)=x^{2},(1,5),5
derivative of 7^xln^2(7)	\frac{d}{dx}(7^{x}\ln^{2}(7))
derivative of arccsc(2x^4-5)	derivative\:\arccsc(2x^{4}-5)
derivative of 2/3 x^3-8x-15	\frac{d}{dx}(\frac{2}{3}x^{3}-8x-15)
area x^2-11,10x,[-sqrt(11),0]	area\:x^{2}-11,10x,[-\sqrt{11},0]
limit as x approaches infinity of 4+3/x	\lim\:_{x\to\:\infty\:}(4+\frac{3}{x})
integral of sin(4x)\sqrt[3]{cos(4x)}	\int\:\sin(4x)\sqrt[3]{\cos(4x)}dx
integral of (9x^2)/((100+x^2)^2)	\int\:\frac{9x^{2}}{(100+x^{2})^{2}}dx
integral of pi/4	\int\:\frac{π}{4}
(\partial)/(\partial x)(x^3e^{sqrt(3xy)})	\frac{\partial\:}{\partial\:x}(x^{3}e^{\sqrt{3xy}})
integral from-infinity to 0 of 3^r	\int\:_{-\infty\:}^{0}3^{r}dr
integral from 0 to 2 of 1/(1-x)	\int\:_{0}^{2}\frac{1}{1-x}dx
derivative of 3x^2+4x+5	\frac{d}{dx}(3x^{2}+4x+5)
limit as x approaches 0 of (x^2)/(1+x^2)	\lim\:_{x\to\:0}(\frac{x^{2}}{1+x^{2}})
laplacetransform 3(t-pi)	laplacetransform\:3(t-π)

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