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Popular Calculus Problems

derivative of f(x)=1x^3	derivative\:f(x)=1x^{3}
derivative of 8sin((2pi/3))	\frac{d}{dx}(8\sin(\frac{2π}{3}))
integral of (2x)/(3x-5)	\int\:\frac{2x}{3x-5}dx
sum from n=1 to infinity of (n+2)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{n+2}{n+1}
integral of ((1-cos^3(x))sin(x))	\int\:((1-\cos^{3}(x))\sin(x))dx
integral of (sin^9(x))cos(x)	\int\:(\sin^{9}(x))\cos(x)dx
limit as x approaches 0 of (sin(6x))/x	\lim\:_{x\to\:0}(\frac{\sin(6x)}{x})
integral of λe^{-λx}	\int\:λe^{-λx}dx
integral of 2sin(2t)	\int\:2\sin(2t)dt
limit as z approaches 1 of (z-1)/(z^2-1)	\lim\:_{z\to\:1}(\frac{z-1}{z^{2}-1})
limit as x approaches 0 of e^{3x}-1-3x	\lim\:_{x\to\:0}(e^{3x}-1-3x)
derivative of 1/(4x^4)	derivative\:\frac{1}{4x^{4}}
(dy)/(dx)=4(x^2+1),x(pi/4)=1	\frac{dy}{dx}=4(x^{2}+1),x(\frac{π}{4})=1
derivative of 1-4cos(x)	\frac{d}{dx}(1-4\cos(x))
integral from-2 to 2 of 1/(x^2-9)	\int\:_{-2}^{2}\frac{1}{x^{2}-9}dx
(dv)/(dt)=9.8-v	\frac{dv}{dt}=9.8-v
integral of (x(x-8))/((x-4)^3)	\int\:\frac{x(x-8)}{(x-4)^{3}}dx
limit as x approaches 1 of (2x-7)/(4x+5)	\lim\:_{x\to\:1}(\frac{2x-7}{4x+5})
integral of (-x^2+2x-8)/((x^2+4)(x-2))	\int\:\frac{-x^{2}+2x-8}{(x^{2}+4)(x-2)}dx
integral of (x^2+10x)cos(x)	\int\:(x^{2}+10x)\cos(x)dx
derivative of arcsinh(x^2)	\frac{d}{dx}(\arcsinh(x^{2}))
integral of (2x)/(x^2-6)	\int\:\frac{2x}{x^{2}-6}dx
taylor ln(x),8	taylor\:\ln(x),8
derivative of 1/3 arctan(x/3)	derivative\:\frac{1}{3}\arctan(\frac{x}{3})
derivative of 2e^{-4x^2+3x+7}	\frac{d}{dx}(2e^{-4x^{2}+3x+7})
derivative of f(x)= 7/(sqrt(t))	derivative\:f(x)=\frac{7}{\sqrt{t}}
derivative of ln((4x/(x+9)))	\frac{d}{dx}(\ln(\frac{4x}{x+9}))
integral of 2/(x^2+1)	\int\:\frac{2}{x^{2}+1}dx
integral of 1/(x*sqrt(x^2-1))	\int\:\frac{1}{x\cdot\:\sqrt{x^{2}-1}}dx
derivative of (4x/(x+3))	\frac{d}{dx}(\frac{4x}{x+3})
(dy)/(dx)=5y^2cos(x)	\frac{dy}{dx}=5y^{2}\cos(x)
integral of 10xln(5x)	\int\:10x\ln(5x)dx
integral from 1 to infinity of xe^{-5x}	\int\:_{1}^{\infty\:}xe^{-5x}dx
integral of 7e^xsqrt(2+e^x)	\int\:7e^{x}\sqrt{2+e^{x}}dx
integral of 1/(sqrt(5-8x-x^2))	\int\:\frac{1}{\sqrt{5-8x-x^{2}}}dx
derivative of ln(sqrt(4-3x^3))	\frac{d}{dx}(\ln(\sqrt{4-3x^{3}}))
derivative of (-2x)/((x^2+1)^2)	derivative\:\frac{-2x}{(x^{2}+1)^{2}}
integral of (cos(x))/(3+2sin(x))	\int\:\frac{\cos(x)}{3+2\sin(x)}dx
derivative of sqrt(x+11)	derivative\:\sqrt{x+11}
derivative of 6x-5	\frac{d}{dx}(6x-5)
(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)	\frac{\partial\:}{\partial\:x}(y\sqrt{x}-y^{2}-x+3y)
y^{''}-2y^'+y=2e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=2e^{x}
limit as x approaches-1+of arcsin(x)	\lim\:_{x\to\:-1+}(\arcsin(x))
derivative of (4x+5^2)	\frac{d}{dx}((4x+5)^{2})
f(x)=sin(x^3)	f(x)=\sin(x^{3})
integral of 1/(sqrt(5-7x-3x^2))	\int\:\frac{1}{\sqrt{5-7x-3x^{2}}}dx
derivative of f(x)=2x^3-5x^4	derivative\:f(x)=2x^{3}-5x^{4}
limit as x approaches 0 of (e^{2x-1})/x	\lim\:_{x\to\:0}(\frac{e^{2x-1}}{x})
integral of 4sqrt(4-x^2)	\int\:4\sqrt{4-x^{2}}dx
integral of (x^2-2)sqrt(x^3-6x+3)	\int\:(x^{2}-2)\sqrt{x^{3}-6x+3}dx
integral of 3xe^{7x^2}	\int\:3xe^{7x^{2}}dx
f(x)=16cos(2x)	f(x)=16\cos(2x)
integral of csc^2(x)	\int\:\csc^{2}(x)dx
f(x)=tan((pix)/2)	f(x)=\tan(\frac{πx}{2})
limit as x approaches 0 of (3x^2-4x)/x	\lim\:_{x\to\:0}(\frac{3x^{2}-4x}{x})
integral of ln(2x+7)	\int\:\ln(2x+7)dx
derivative of (sin(x)^{tan(x)})	\frac{d}{dx}((\sin(x))^{\tan(x)})
integral from 0 to e of 2piy(1-ln(y))	\int\:_{0}^{e}2πy(1-\ln(y))dy
integral from-1 to 1 of 1/2 x^3-2x+2	\int\:_{-1}^{1}\frac{1}{2}x^{3}-2x+2dx
integral of 1/(x^3)sin(1/x)	\int\:\frac{1}{x^{3}}\sin(\frac{1}{x})dx
y^{''}-2y^'-3y=24te^{2t},y(0)=5,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=24te^{2t},y(0)=5,y^{\prime\:}(0)=0
derivative of f(x)=(1+sqrt(3x))/(1-sqrt(3x))	derivative\:f(x)=\frac{1+\sqrt{3x}}{1-\sqrt{3x}}
integral of (x^3)/(sqrt(x^2-9))	\int\:\frac{x^{3}}{\sqrt{x^{2}-9}}dx
taylor sin(2x),0	taylor\:\sin(2x),0
d/(dt)((e^{-t})/(1+t^2))	\frac{d}{dt}(\frac{e^{-t}}{1+t^{2}})
derivative of arcsec(x)*arccos(x)	derivative\:\arcsec(x)\cdot\:\arccos(x)
integral of te^{t+2}	\int\:te^{t+2}dt
integral of ()/(m^3+m^2)	\int\:\frac{dm}{m^{3}+m^{2}}dx
d/(d{r)}(1/(2sqrt({r))}+1/(7{r)^{6/7}})	\frac{d}{d{r}}(\frac{1}{2\sqrt{{r}}}+\frac{1}{7{r}^{\frac{6}{7}}})
integral of cos(t)sin^4(t)	\int\:\cos(t)\sin^{4}(t)dt
derivative of e^{-5}	\frac{d}{dx}(e^{-5})
integral of 21x^{20}	\int\:21x^{20}dx
integral of (13)/(x^3-125)	\int\:\frac{13}{x^{3}-125}dx
d/(dθ)(cos(θ^2))	\frac{d}{dθ}(\cos(θ^{2}))
derivative of 2e^x-1	\frac{d}{dx}(2e^{x}-1)
derivative of f(x)=x^2(5x-1)^3	derivative\:f(x)=x^{2}(5x-1)^{3}
derivative of (e^{x^2-1})/(2sqrt(x))	derivative\:\frac{e^{x^{2}-1}}{2\sqrt{x}}
(dy)/(dx)=e^{4x+y}	\frac{dy}{dx}=e^{4x+y}
derivative of y=ln(t(t^2+3)^3)	derivative\:y=\ln(t(t^{2}+3)^{3})
integral of (2x)/(x^2-9)	\int\:\frac{2x}{x^{2}-9}dx
derivative of-4e^{-2x}	\frac{d}{dx}(-4e^{-2x})
f(x)=((tan(x)-1))/(sec(x))	f(x)=\frac{(\tan(x)-1)}{\sec(x)}
derivative of 3^{9x}	derivative\:3^{9x}
limit as x approaches infinity of (3^x+2^x)^{1/x}	\lim\:_{x\to\:\infty\:}((3^{x}+2^{x})^{\frac{1}{x}})
derivative of ((x^6+1))/(x^5)	derivative\:\frac{(x^{6}+1)}{x^{5}}
integral of (e^x)/(sqrt(1-81e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-81e^{2x}}}dx
tangent of y=x^3-2x+2,(2,6)	tangent\:y=x^{3}-2x+2,(2,6)
integral of cot^{(-5)/4}(2x)csc^4(2x)	\int\:\cot^{\frac{-5}{4}}(2x)\csc^{4}(2x)dx
derivative of a^9+cos^9(x)	derivative\:a^{9}+\cos^{9}(x)
integral of ((sec^2(1/x)))/(x^2)	\int\:\frac{(\sec^{2}(\frac{1}{x}))}{x^{2}}dx
integral of t^2e^{-t/2}	\int\:t^{2}e^{-\frac{t}{2}}dt
derivative of-5x^2-4cos(x)	\frac{d}{dx}(-5x^{2}-4\cos(x))
integral of 2xe^{-8x}	\int\:2xe^{-8x}dx
sum from n=0 to infinity of 300(-1.41)^n	\sum\:_{n=0}^{\infty\:}300(-1.41)^{n}
integral of (sin(20)(x))/(sin(10)(x))	\int\:\frac{\sin(20)(x)}{\sin(10)(x)}dx
derivative of 6cos(3x+3)	derivative\:6\cos(3x+3)
derivative of y=e^{7x}	derivative\:y=e^{7x}
laplacetransform e^{2t}cos(2t)	laplacetransform\:e^{2t}\cos(2t)
derivative of 1-10x	\frac{d}{dx}(1-10x)
y^{''}-5y^'=(5t+9)sin(2t)	y^{\prime\:\prime\:}-5y^{\prime\:}=(5t+9)\sin(2t)

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