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Popular Calculus Problems

integral from 0 to 100 of 1/(sqrt(x))	\int\:_{0}^{100}\frac{1}{\sqrt{x}}dx
integral from 0 to 1 of 2x	\int\:_{0}^{1}2xdx
derivative of y=4^{x+1}	derivative\:y=4^{x+1}
6y^{''}+2y^'=0,y^'(0)=4	6\cdot\:y^{\prime\:\prime\:}+2\cdot\:y^{\prime\:}=0,y^{\prime\:}(0)=4
integral from 0 to 1 of (2(x+2))/5	\int\:_{0}^{1}\frac{2(x+2)}{5}dx
derivative of tan(2^x)	derivative\:\tan(2^{x})
derivative of (7x^2-11xe^x)	\frac{d}{dx}((7x^{2}-11x)e^{x})
limit as x approaches 8-of (2x)/(x+8)	\lim\:_{x\to\:8-}(\frac{2x}{x+8})
y^'-1/x y=(1+ln(x))y^3	y^{\prime\:}-\frac{1}{x}y=(1+\ln(x))y^{3}
slope of f(x)=4x^2	slope\:f(x)=4x^{2}
derivative of x^3-x^2-x+2	\frac{d}{dx}(x^{3}-x^{2}-x+2)
derivative of arcsin(3xln(sqrt(x+1)))	\frac{d}{dx}(\arcsin(3x)\ln(\sqrt{x+1}))
integral of 3xzy+xy^2+2zx^2	\int\:3xzy+xy^{2}+2zx^{2}
derivative of log_{x}(x^2+1)	\frac{d}{dx}(\log_{x}(x^{2}+1))
integral of ((x^2+4))/((x-5)(x^2+9))	\int\:\frac{(x^{2}+4)}{(x-5)(x^{2}+9)}dx
integral of x^4e^{(1-x^5)}	\int\:x^{4}e^{(1-x^{5})}dx
(dy)/(dx)+5y=8	\frac{dy}{dx}+5y=8
derivative of sin(x^2+sin(x^2+sin(x^2)))	\frac{d}{dx}(\sin(x^{2}+\sin(x^{2}+\sin(x^{2}))))
integral of 16x^2	\int\:16x^{2}dx
derivative of x\|x\|^{\|x\|-1}(ln\|x\|+1)	\frac{d}{dx}(x\left\|x\right\|^{\left\|x\right\|-1}(\ln\left\|x\right\|+1))
tangent of f(x)=x^3,\at =0	tangent\:f(x)=x^{3},\at\:=0
limit as x approaches 4+of cx^2+3x	\lim\:_{x\to\:4+}(cx^{2}+3x)
integral of arccot(6y)	\int\:\arccot(6y)dy
limit as x approaches 0+of x^{tan(x)}	\lim\:_{x\to\:0+}(x^{\tan(x)})
integral of ((ln(x))^2)	\int\:((\ln(x))^{2})dx
derivative of 4x^2tan(x)	derivative\:4x^{2}\tan(x)
(\partial)/(\partial x)(xexp(x,y,z)(-x^2-y^2-z^2))	\frac{\partial\:}{\partial\:x}(xexp(x,y,z)(-x^{2}-y^{2}-z^{2}))
tangent of f(x)=-4sin(x),\at x=pi	tangent\:f(x)=-4\sin(x),\at\:x=π
integral of (sech^2(x))/(tanh(x))	\int\:\frac{\sech^{2}(x)}{\tanh(x)}dx
integral from 0 to 1 of (x^2+5)e^{-x}	\int\:_{0}^{1}(x^{2}+5)e^{-x}dx
integral of (1000)/(sqrt(100x))	\int\:\frac{1000}{\sqrt{100x}}dx
integral from 0 to 3-x of 3-x-y	\int\:_{0}^{3-x}3-x-ydy
derivative of xtan(1/x)	\frac{d}{dx}(x\tan(\frac{1}{x}))
integral of 1/((x+3)^2(x-5))	\int\:\frac{1}{(x+3)^{2}(x-5)}dx
derivative of (-6/(\sqrt[5]{x^3)})	\frac{d}{dx}(\frac{-6}{\sqrt[5]{x^{3}}})
derivative of cos^3(12x)	derivative\:\cos^{3}(12x)
normal of y=sqrt(3x^2+2x),(2,4)	normal\:y=\sqrt{3x^{2}+2x},(2,4)
integral of sin^2(xco)s^2x	\int\:\sin^{2}(xco)s^{2}xdx
y^{''}-6y^'+9y=0,y(0)=6,y^'(0)=0	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=6,y^{\prime\:}(0)=0
f(x)=(sin(x))/(2+cos(x))	f(x)=\frac{\sin(x)}{2+\cos(x)}
limit as x approaches 0 of sqrt(x^2+1)	\lim\:_{x\to\:0}(\sqrt{x^{2}+1})
(dy)/(dx)=x+4	\frac{dy}{dx}=x+4
derivative of 30e^xsqrt(x)	derivative\:30e^{x}\sqrt{x}
integral from 0 to 1 of (u+2)(u-3)	\int\:_{0}^{1}(u+2)(u-3)du
integral of (x^2ln^3(1+x^3))/(1+x^3)	\int\:\frac{x^{2}\ln^{3}(1+x^{3})}{1+x^{3}}dx
limit as x approaches 0 of 1/(2^x)	\lim\:_{x\to\:0}(\frac{1}{2^{x}})
parity sin(tan(2x))	parity\:\sin(\tan(2x))
integral of 3x(x^2-1/3)	\int\:3x(x^{2}-\frac{1}{3})dx
tangent of f(x)= x/(x+1),\at x=-2	tangent\:f(x)=\frac{x}{x+1},\at\:x=-2
(\partial)/(\partial x)(-1/(2x^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{2x^{2}})
integral of 1+1/((x+1)^2)	\int\:1+\frac{1}{(x+1)^{2}}dx
derivative of sin^{-1}(x)	\frac{d}{dx}(\sin^{-1}(x))
integral of sec^2(X)	\int\:\sec^{2}(X)dX
limit as x approaches-3-of 3/(x^2-9)	\lim\:_{x\to\:-3-}(\frac{3}{x^{2}-9})
integral of (3e^x+5sin(x))	\int\:(3e^{x}+5\sin(x))dx
integral from 1 to 2 of xsin(x^2)	\int\:_{1}^{2}x\sin(x^{2})dx
derivative of (72/x)	\frac{d}{dx}(\frac{72}{x})
integral from 0 to pi of (cos(2x))^4	\int\:_{0}^{π}(\cos(2x))^{4}dx
integral of 3x*e^{(-4x)}	\int\:3x\cdot\:e^{(-4x)}dx
derivative of (x^2y/(x^2+y^2))	\frac{d}{dx}(\frac{x^{2}y}{x^{2}+y^{2}})
derivative of y=\|x^2-8\|	derivative\:y=\left\|x^{2}-8\right\|
y^{''}-3y^'+2y=4x^2	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=4x^{2}
integral of x/(2sqrt(x))	\int\:\frac{x}{2\sqrt{x}}dx
limit as x approaches infinity of x/k	\lim\:_{x\to\:\infty\:}(\frac{x}{k})
derivative of 6x^2-x	\frac{d}{dx}(6x^{2}-x)
(\partial)/(\partial y)(xsin(yz))	\frac{\partial\:}{\partial\:y}(x\sin(yz))
tangent of x^2-sqrt(x)	tangent\:x^{2}-\sqrt{x}
limit as x approaches 0 of (\|x\|)/(2x)	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{2x})
(\partial)/(\partial x)(2y+xy+ye^y-e^y)	\frac{\partial\:}{\partial\:x}(2y+xy+ye^{y}-e^{y})
integral of 5/(x^2-1)	\int\:\frac{5}{x^{2}-1}dx
derivative of 2^x+x	\frac{d}{dx}(2^{x}+x)
limit as x approaches 2 of 1/(x^2)	\lim\:_{x\to\:2}(\frac{1}{x^{2}})
limit as x approaches pi of x/3-(2pi)/3	\lim\:_{x\to\:π}(\frac{x}{3}-\frac{2π}{3})
(d^2x)/(dt^2)+4x=t^2	\frac{d^{2}x}{dt^{2}}+4x=t^{2}
simplify sqrt(((5-120x)^2+(150x)^2))	simplify\:\sqrt{((5-120x)^{2}+(150x)^{2})}
integral from 0 to 1 of (x+1)	\int\:_{0}^{1}(x+1)dx
integral of-xcos(x+pi/3)+xcos(x)	\int\:-x\cos(x+\frac{π}{3})+x\cos(x)dx
integral of 1/(y(1-y/m))	\int\:\frac{1}{y(1-\frac{y}{m})}dy
integral of 5t^4	\int\:5t^{4}dt
integral of (x^2-12x-1)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-12x-1}{(x-1)^{2}(x^{2}+1)}dx
derivative of mx+c	\frac{d}{dx}(mx+c)
derivative of e^xsin(8x)	\frac{d}{dx}(e^{x}\sin(8x))
laplacetransform 1-2e^{-4t}	laplacetransform\:1-2e^{-4t}
integral of 1/(x-x^2+2)	\int\:\frac{1}{x-x^{2}+2}dx
integral of (2+x)/x	\int\:\frac{2+x}{x}dx
derivative of e^{aarccos(x})	\frac{d}{dx}(e^{a\arccos(x)})
area 2cos(9x),2-2cos(9x),[0, pi/9 ]	area\:2\cos(9x),2-2\cos(9x),[0,\frac{π}{9}]
integral of 6arctan(sqrt(x))	\int\:6\arctan(\sqrt{x})dx
limit as x approaches 8+of 1/(\|8-x\|)	\lim\:_{x\to\:8+}(\frac{1}{\left\|8-x\right\|})
taylor sin(8x)	taylor\:\sin(8x)
(dy)/(dx)=b-ay	\frac{dy}{dx}=b-ay
y^'=x(1+y^2)	y^{\prime\:}=x(1+y^{2})
tangent of y=t^3-36t+4,(6,4)	tangent\:y=t^{3}-36t+4,(6,4)
limit as x approaches 0-of e^{4/(x^5)}	\lim\:_{x\to\:0-}(e^{\frac{4}{x^{5}}})
integral of (x^2-6)/((x+2)(2x-1))	\int\:\frac{x^{2}-6}{(x+2)(2x-1)}dx
area y=x^2,y=sqrt(6+x)	area\:y=x^{2},y=\sqrt{6+x}
derivative of log_{e}(4x)	\frac{d}{dx}(\log_{e}(4x))
derivative of (8(4x^4+5)^3)	\frac{d}{dx}((8(4x)^{4}+5)^{3})
(\partial)/(\partial y)(arctan(x)y)	\frac{\partial\:}{\partial\:y}(\arctan(x)y)
tangent of 4-ln(x)	tangent\:4-\ln(x)

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