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Popular Calculus Problems

derivative of y=((x^7-4x^3+12x))/(x^3)	derivative\:y=\frac{(x^{7}-4x^{3}+12x)}{x^{3}}
limit as x approaches 1+of x^{9/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{9}{1-x}})
derivative of 2sin(3pix)	derivative\:2\sin(3πx)
y^'+2/x y=x,y(1)=0	y^{\prime\:}+\frac{2}{x}y=x,y(1)=0
tangent of y=e^x	tangent\:y=e^{x}
parity x*tan(x)	parity\:x\cdot\:\tan(x)
laplacetransform t*cos(t)	laplacetransform\:t\cdot\:\cos(t)
derivative of sinh^3(1/x)	\frac{d}{dx}(\sinh^{3}(\frac{1}{x}))
integral of (sin(x)-6cos(x))	\int\:(\sin(x)-6\cos(x))dx
integral from 1 to infinity of 2/x	\int\:_{1}^{\infty\:}\frac{2}{x}dx
integral of (y^2+1)/y	\int\:\frac{y^{2}+1}{y}dy
derivative of (x^2-3x+4^4)	\frac{d}{dx}((x^{2}-3x+4)^{4})
taylor 1/(1-e^x)	taylor\:\frac{1}{1-e^{x}}
sum from n=0 to infinity of (3+2n)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{3+2n}{2^{n}}
sum from n=0 to infinity of 1/(n+13)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+13}
integral of y/((y^2-4)^{2/5)}	\int\:\frac{y}{(y^{2}-4)^{\frac{2}{5}}}dy
integral of-cos(nx)	\int\:-\cos(nx)dx
(dy)/(dx)=(x^3+y^3)/(xy^2)	\frac{dy}{dx}=\frac{x^{3}+y^{3}}{xy^{2}}
integral of 4sqrt(x)+\sqrt[4]{x}	\int\:4\sqrt{x}+\sqrt[4]{x}dx
integral from 0 to 1/2 of 8x-1/2 x	\int\:_{0}^{\frac{1}{2}}8x-\frac{1}{2}xdx
limit as x approaches-2 of x^5+4x^3-5x-2	\lim\:_{x\to\:-2}(x^{5}+4x^{3}-5x-2)
(1+cos(x))^'	(1+\cos(x))^{\prime\:}
integral from 0 to 3 of \|x-1\|	\int\:_{0}^{3}\left\|x-1\right\|dx
integral from 0 to 1 of sqrt(1+x^2)	\int\:_{0}^{1}\sqrt{1+x^{2}}dx
integral from 0 to 5 of pi(2x)^2	\int\:_{0}^{5}π(2x)^{2}dx
integral of ((sec^2(x)))/(tan^2(x))	\int\:\frac{(\sec^{2}(x))}{\tan^{2}(x)}dx
derivative of y=(1/(cos^2(x)))	\frac{d}{dx}y=(\frac{1}{\cos^{2}(x)})
limit as x approaches-9 of (8x+72)/(\|x+9\|)	\lim\:_{x\to\:-9}(\frac{8x+72}{\left\|x+9\right\|})
inverse oflaplace ((2*s))/(s^2+6s+13)	inverselaplace\:\frac{(2\cdot\:s)}{s^{2}+6s+13}
d/(dθ)((-1+cos(θ))sin(θ))	\frac{d}{dθ}((-1+\cos(θ))\sin(θ))
integral of x^4(3x^5+1)^9	\int\:x^{4}(3x^{5}+1)^{9}dx
derivative of \|x-8\|	\frac{d}{dx}(\left\|x-8\right\|)
limit as x approaches infinity of x^0	\lim\:_{x\to\:\infty\:}(x^{0})
taylor x^4	taylor\:x^{4}
sum from n=1 to infinity of 4/3 (5/7)^n	\sum\:_{n=1}^{\infty\:}\frac{4}{3}(\frac{5}{7})^{n}
integral of 14sin^3(xco)s^2x	\int\:14\sin^{3}(xco)s^{2}xdx
integral of x^2-19	\int\:x^{2}-19dx
area x^2-2,2	area\:x^{2}-2,2
integral of 2xsec^2(5x)	\int\:2x\sec^{2}(5x)dx
integral of x^2-4x+5	\int\:x^{2}-4x+5dx
limit as x approaches 0-of x/(ln(x))	\lim\:_{x\to\:0-}(\frac{x}{\ln(x)})
integral of 1/(8x+5)	\int\:\frac{1}{8x+5}dx
derivative of ln({f}(x)*{f}(x)(sin(x)))	\frac{d}{dx}(\ln({f}(x))\cdot\:{f}(x)(\sin(x)))
integral of (-(2x)/(1+x^2))	\int\:(-\frac{2x}{1+x^{2}})dx
integral of 4x+3/(sqrt(x))	\int\:4x+\frac{3}{\sqrt{x}}dx
inverse oflaplace cos(2t)	inverselaplace\:\cos(2t)
taylor (1-x^2)^{-3/2}	taylor\:(1-x^{2})^{-\frac{3}{2}}
x^2y^'-x=1+y+xy	x^{2}y^{\prime\:}-x=1+y+xy
integral from-1 to 3 of (5-1/4 x^3)	\int\:_{-1}^{3}(5-\frac{1}{4}x^{3})dx
integral of (7x^2)/(1+x^6)	\int\:\frac{7x^{2}}{1+x^{6}}dx
(x^2y^2-x^4)y^'=x^2y^2-y^4	(x^{2}y^{2}-x^{4})y^{\prime\:}=x^{2}y^{2}-y^{4}
limit as x approaches-1 of ln(1+x)	\lim\:_{x\to\:-1}(\ln(1+x))
derivative of ln(4x-5)	\frac{d}{dx}(\ln(4x-5))
taylor 1/(1-x-x^2)	taylor\:\frac{1}{1-x-x^{2}}
derivative of sqrt(t)-2	derivative\:\sqrt{t}-2
tangent of f(x)=x^2+4,\at x=-1	tangent\:f(x)=x^{2}+4,\at\:x=-1
integral of ((x^2-x+18))/(x^3+3x)	\int\:\frac{(x^{2}-x+18)}{x^{3}+3x}dx
integral of (3x^4)	\int\:(3x^{4})dx
tangent of f(x)=sqrt(x-3),\at x=7	tangent\:f(x)=\sqrt{x-3},\at\:x=7
2ty^'=8y	2ty^{\prime\:}=8y
derivative of 8ln(sin(x))	\frac{d}{dx}(8\ln(\sin(x)))
integral of e^{6x}(6)	\int\:e^{6x}(6)dx
d/(dy)(1/(xy))	\frac{d}{dy}(\frac{1}{xy})
integral of (6t^3-t^2+24t)/(t^2+4)	\int\:\frac{6t^{3}-t^{2}+24t}{t^{2}+4}dt
inverse oflaplace-(5s)/(((s+1)^2+3))	inverselaplace\:-\frac{5s}{((s+1)^{2}+3)}
derivative of e^{x^3}y	\frac{d}{dx}(e^{x^{3}}y)
integral of 10x^{3/2}+6sqrt(x)-8	\int\:10x^{\frac{3}{2}}+6\sqrt{x}-8dx
integral of 5/x+sec^2(x)	\int\:\frac{5}{x}+\sec^{2}(x)dx
limit as x approaches 1 of (-3x)/(x-1)	\lim\:_{x\to\:1}(\frac{-3x}{x-1})
v'=v^2	v\prime\:=v^{2}
limit as x approaches 2 of 2x^2	\lim\:_{x\to\:2}(2x^{2})
(dx)/(dt)=-x(x+2),x(0)=1	\frac{dx}{dt}=-x(x+2),x(0)=1
d/(dy)(3xy^2)	\frac{d}{dy}(3xy^{2})
(\partial)/(\partial x)((2x-y)^4)	\frac{\partial\:}{\partial\:x}((2x-y)^{4})
integral from 0 to pi of (pi-x)cos(nx)	\int\:_{0}^{π}(π-x)\cos(nx)dx
limit as x approaches 6 of sqrt(x-10)	\lim\:_{x\to\:6}(\sqrt{x-10})
y^{''}+5y^'-6y=0	y^{\prime\:\prime\:}+5y^{\prime\:}-6y=0
derivative of y=ln(2+x)+2/(2+x)	derivative\:y=\ln(2+x)+\frac{2}{2+x}
derivative of sqrt(6x-1)	derivative\:\sqrt{6x-1}
(\partial)/(\partial x)(sin(x)+pi*cos(y))	\frac{\partial\:}{\partial\:x}(\sin(x)+π\cdot\:\cos(y))
x(dy)/(dx)+2y=sin(x)	x\frac{dy}{dx}+2y=\sin(x)
integral of (e^{8sqrt(x)})/(sqrt(x))	\int\:\frac{e^{8\sqrt{x}}}{\sqrt{x}}dx
integral of (sin(21x))/(1+cos^2(21x))	\int\:\frac{\sin(21x)}{1+\cos^{2}(21x)}dx
integral from 0 to 1 of x(1-x)	\int\:_{0}^{1}x(1-x)dx
area 6x^2,x^2+8	area\:6x^{2},x^{2}+8
limit as x approaches 0 of (14)/(tan(x))	\lim\:_{x\to\:0}(\frac{14}{\tan(x)})
laplacetransform Q	laplacetransform\:Q
limit as x approaches 0 of (ln(1+4x))/x	\lim\:_{x\to\:0}(\frac{\ln(1+4x)}{x})
integral of x^{11}sqrt(x^6+5)	\int\:x^{11}\sqrt{x^{6}+5}dx
derivative of ln(x-6)	derivative\:\ln(x-6)
x^2y^{''}-20y=0	x^{2}y^{\prime\:\prime\:}-20y=0
d/(dθ)({r}(θ)(1-cos(θ)))	\frac{d}{dθ}({r}(θ)(1-\cos(θ)))
derivative of ln((3x+1(x+2)^2))	\frac{d}{dx}(\ln((3x+1)(x+2)^{2}))
derivative of e^{-2x}cos(x)	\frac{d}{dx}(e^{-2x}\cos(x))
tangent of y=3+4x+7xe^x	tangent\:y=3+4x+7xe^{x}
integral of tan(x)(4cos(x)+8sec(x))	\int\:\tan(x)(4\cos(x)+8\sec(x))dx
(dy)/(dx)+y^5x+6y=0	\frac{dy}{dx}+y^{5}x+6y=0
integral of 1/(x^2sqrt(4-x^2))	\int\:\frac{1}{x^{2}\sqrt{4-x^{2}}}dx
derivative of 3xe^x-cos(x)	\frac{d}{dx}(3xe^{x}-\cos(x))
derivative of f(t)=sqrt(5-t)	derivative\:f(t)=\sqrt{5-t}

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