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Popular Calculus Problems

integral from-2 to-1 of e^{-(x+1)}	\int\:_{-2}^{-1}e^{-(x+1)}dx
tangent of 6/(5x+3)	tangent\:\frac{6}{5x+3}
derivative of u(x)=2x	derivative\:u(x)=2x
derivative of cos(e^{3x}-sin(e^{3x}))	\frac{d}{dx}(\cos(e^{3x})-\sin(e^{3x}))
integral of 5sin(x)ln(sin(x))	\int\:5\sin(x)\ln(\sin(x))dx
sum from n=0 to infinity of n^{0.5}	\sum\:_{n=0}^{\infty\:}n^{0.5}
integral of (x/(sqrt(x)))	\int\:(\frac{x}{\sqrt{x}})dx
(\partial)/(\partial x)((2x)^x)	\frac{\partial\:}{\partial\:x}((2x)^{x})
derivative of (tan(x)dx)	\frac{d}{dx}((\tan(x))dx)
(dy)/(dx)-2y+x^2=0	\frac{dy}{dx}-2y+x^{2}=0
integral from 1 to 11 of 1/(x-7)	\int\:_{1}^{11}\frac{1}{x-7}dx
derivative of (sqrt(x)+5x(x^{3/2}-x))	\frac{d}{dx}((\sqrt{x}+5x)(x^{\frac{3}{2}}-x))
derivative of f(x)=3x^4-12x^3+4	derivative\:f(x)=3x^{4}-12x^{3}+4
maclaurin (1+x^2)^{1/2}	maclaurin\:(1+x^{2})^{\frac{1}{2}}
integral of 3x^2cos(x^3+2)	\int\:3x^{2}\cos(x^{3}+2)dx
integral of 9e^{0.01x}	\int\:9e^{0.01x}dx
derivative of (2x/((x+1)^2))	\frac{d}{dx}(\frac{2x}{(x+1)^{2}})
derivative of 3x^2-7x+10	\frac{d}{dx}(3x^{2}-7x+10)
tangent of f(x)=2x^2+5x-3	tangent\:f(x)=2x^{2}+5x-3
integral of 1/((x^2-1)(x-3))	\int\:\frac{1}{(x^{2}-1)(x-3)}dx
integral of 2sqrt(x-2)	\int\:2\sqrt{x-2}dx
y^'+y/t =t^2y^4	y^{\prime\:}+\frac{y}{t}=t^{2}y^{4}
tangent of x^2+5x,\at x=4	tangent\:x^{2}+5x,\at\:x=4
limit as x approaches+4+of 7/(x-4)	\lim\:_{x\to\:+4+}(\frac{7}{x-4})
integral of sqrt(1-25x^2)	\int\:\sqrt{1-25x^{2}}dx
integral of (20x^4)/(4x^5+3)	\int\:\frac{20x^{4}}{4x^{5}+3}dx
integral of 3x(x^2+2)^5	\int\:3x(x^{2}+2)^{5}dx
derivative of (x^2-3x/(x+1))	\frac{d}{dx}(\frac{x^{2}-3x}{x+1})
derivative of (\sqrt[3]{x}+8(7x^{-1}-8))	\frac{d}{dx}((\sqrt[3]{x}+8)(7x^{-1}-8))
integral of (x^6-x^3+16)/(x^4+4x^2)	\int\:\frac{x^{6}-x^{3}+16}{x^{4}+4x^{2}}dx
t(dy)/(dt)=t^3+15t^3y	t\frac{dy}{dt}=t^{3}+15t^{3}y
-6y^'+18x^2=0	-6y^{\prime\:}+18x^{2}=0
(t^3)dx+(xt^2+x^3)dt=0	(t^{3})dx+(xt^{2}+x^{3})dt=0
integral of ((1-x^3))/((x\sqrt[3]{x))}	\int\:\frac{(1-x^{3})}{(x\sqrt[3]{x})}dx
integral of cos(x)-cos^3(x)	\int\:\cos(x)-\cos^{3}(x)dx
derivative of-4x^{-3}	\frac{d}{dx}(-4x^{-3})
integral of 11x^{4/7}+7x^{-6/7}	\int\:11x^{\frac{4}{7}}+7x^{-\frac{6}{7}}dx
tangent of y=x^4	tangent\:y=x^{4}
integral of x/4 sqrt(16+x^2)	\int\:\frac{x}{4}\sqrt{16+x^{2}}dx
limit as x approaches 0-of 1/(e^x+1)	\lim\:_{x\to\:0-}(\frac{1}{e^{x}+1})
derivative of (x^3/6-(3x^2)/2)	\frac{d}{dx}(\frac{x^{3}}{6}-\frac{3x^{2}}{2})
integral of 1.2	\int\:1.2
integral of sin^3(3x)sqrt(cos(3x))	\int\:\sin^{3}(3x)\sqrt{\cos(3x)}dx
integral of sec^2(x)csc^2(x)	\int\:\sec^{2}(x)\csc^{2}(x)dx
integral from 0 to infinity of e^{-xt}	\int\:_{0}^{\infty\:}e^{-xt}dt
integral of 16t^3	\int\:16t^{3}dt
integral from 1/2 to 7 of 10xln(2x)	\int\:_{\frac{1}{2}}^{7}10x\ln(2x)dx
integral from 0 to 4 of 3e^{-x^2}	\int\:_{0}^{4}3e^{-x^{2}}dx
derivative of f(x)=9	derivative\:f(x)=9
integral of cot(m)xcsc^2(m)x	\int\:\cot(m)x\csc^{2}(m)xdx
tangent of f(x)=2x^3,\at x=-1	tangent\:f(x)=2x^{3},\at\:x=-1
integral of sin(x/5)	\int\:\sin(\frac{x}{5})dx
tangent of ax^3,\at x=-5	tangent\:ax^{3},\at\:x=-5
derivative of y=3arctan(x-sqrt(1+x^2))	derivative\:y=3\arctan(x-\sqrt{1+x^{2}})
(\partial)/(\partial y)(y^3cos(x+y))	\frac{\partial\:}{\partial\:y}(y^{3}\cos(x+y))
integral of (2x^3+10x^2-3x+4)	\int\:(2x^{3}+10x^{2}-3x+4)dx
y^{''}-6y^'=4t	y^{\prime\:\prime\:}-6y^{\prime\:}=4t
derivative of (2x+1/(3x-1))	\frac{d}{dx}(\frac{2x+1}{3x-1})
integral of (x-1)(x+2)(x+4)	\int\:(x-1)(x+2)(x+4)dx
(dy}{dx}=\frac{(y-sqrt(x^2+y^2)))/x	\frac{dy}{dx}=\frac{(y-\sqrt{x^{2}+y^{2}})}{x}
yy^'=(y^2-y)(2x+5)	yy^{\prime\:}=(y^{2}-y)(2x+5)
integral of sin(3x)-cos(3x)	\int\:\sin(3x)-\cos(3x)dx
y^{''}+4y^'+5y=10	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=10
derivative of 3x^2+2e^x	\frac{d}{dx}(3x^{2}+2e^{x})
derivative of h(x)=sec(-4x^2-3x+2)	derivative\:h(x)=\sec(-4x^{2}-3x+2)
normal of f(x)=3sin(2x),\at x= pi/8	normal\:f(x)=3\sin(2x),\at\:x=\frac{π}{8}
x(dy)/(dx)=5xe^x-y+9x^2	x\frac{dy}{dx}=5xe^{x}-y+9x^{2}
integral of (ln(x)+3)/(x(ln(x)-1))	\int\:\frac{\ln(x)+3}{x(\ln(x)-1)}dx
laplacetransform sin(t-5)	laplacetransform\:\sin(t-5)
derivative of y=(3x^2+3x-1)^4	derivative\:y=(3x^{2}+3x-1)^{4}
(x^2-3y^2)dx+(2xy)dy=0	(x^{2}-3y^{2})dx+(2xy)dy=0
derivative of (sqrt(x)/x)	\frac{d}{dx}(\frac{\sqrt{x}}{x})
tangent of f(x)=4x^2-4x+1,(-1,8)	tangent\:f(x)=4x^{2}-4x+1,(-1,8)
(\partial)/(\partial x)(y-(27)/(x^2))	\frac{\partial\:}{\partial\:x}(y-\frac{27}{x^{2}})
integral of (2sin(x)-5e^x)	\int\:(2\sin(x)-5e^{x})dx
integral of 1/2 sin(2θ)	\int\:\frac{1}{2}\sin(2θ)dθ
(\partial)/(\partial x)(x^2+2y^2-x^2y-1)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}-x^{2}y-1)
y^{''}+81y=cos(4t)	y^{\prime\:\prime\:}+81y=\cos(4t)
d/(dt)(1/3 pi{r}(t)(t)^2h)	\frac{d}{dt}(\frac{1}{3}π{r}(t)(t)^{2}h)
(\partial)/(\partial x)((7x-5y)/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{7x-5y}{y^{2}+x^{2}})
limit as x approaches-pi of (x+pi)csc(x)	\lim\:_{x\to\:-π}((x+π)\csc(x))
8t(dy)/(dt)+y=t^7	8t\frac{dy}{dt}+y=t^{7}
derivative of (x^2/(sqrt(x^4+x^2+1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{4}+x^{2}+1}})
derivative of arcsin(sin(x-cos(x)))	\frac{d}{dx}(\arcsin(\sin(x)-\cos(x)))
tangent of (10x^3)/3+(13x^2)/2+4x+16	tangent\:\frac{10x^{3}}{3}+\frac{13x^{2}}{2}+4x+16
integral of cos(t/2)	\int\:\cos(\frac{t}{2})dt
derivative of x^2-8x+13	\frac{d}{dx}(x^{2}-8x+13)
derivative of (2x/(x^2))	\frac{d}{dx}(\frac{2x}{x^{2}})
y^3-(10x+4)+3xy^2y^'=0	y^{3}-(10x+4)+3xy^{2}y^{\prime\:}=0
derivative of (3a+1)^2	derivative\:(3a+1)^{2}
integral from 1 to 9 of sqrt(x)ln(x)	\int\:_{1}^{9}\sqrt{x}\ln(x)dx
integral of (cos(a)x)/(sqrt(b+sin(a)x))	\int\:\frac{\cos(a)x}{\sqrt{b+\sin(a)x}}dx
integral of xsec(x)tan(x)	\int\:x\cdot\:\sec(x)\cdot\:\tan(x)dx
integral of (3x^5+1)/(3x-3x^5)	\int\:\frac{3x^{5}+1}{3x-3x^{5}}dx
derivative of ln(1-x^2)	derivative\:\ln(1-x^{2})
integral of (sin(2x)+cos(2x))^2	\int\:(\sin(2x)+\cos(2x))^{2}dx
derivative of x^{-1/2}	derivative\:x^{-\frac{1}{2}}
area y=3-x,y=2x^2,[0,1]	area\:y=3-x,y=2x^{2},[0,1]
tangent of f(x)=2x^2+3x,(-2,2)	tangent\:f(x)=2x^{2}+3x,(-2,2)
(\partial)/(\partial x)(x^3-12x+y^3-27y)	\frac{\partial\:}{\partial\:x}(x^{3}-12x+y^{3}-27y)

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