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Popular Calculus Problems

integral of 5/(3x+1)	\int\:\frac{5}{3x+1}dx
sum from n=1 to infinity of 1/(2n!)	\sum\:_{n=1}^{\infty\:}\frac{1}{2n!}
integral of-1+ln(x)	\int\:-1+\ln(x)dx
integral of 64x^3(4x^2-1)^3	\int\:64x^{3}(4x^{2}-1)^{3}dx
derivative of x^{4/5}(x-8^2)	\frac{d}{dx}(x^{\frac{4}{5}}(x-8)^{2})
integral from-1 to 6 of \|x-4x^2\|	\int\:_{-1}^{6}\left\|x-4x^{2}\right\|dx
y^{''}-(2/t)y^'+(2/(t^2))y=0	y^{\prime\:\prime\:}-(\frac{2}{t})y^{\prime\:}+(\frac{2}{t^{2}})y=0
integral of (ln(y))^2y	\int\:(\ln(y))^{2}ydy
derivative of (x^2+4)/(x^2-4)	derivative\:\frac{x^{2}+4}{x^{2}-4}
area 6-6x^2,0	area\:6-6x^{2},0
derivative of-3/(8x^{5/2})	\frac{d}{dx}(-\frac{3}{8x^{\frac{5}{2}}})
integral of sec^2(5x)+e^{x/2}	\int\:\sec^{2}(5x)+e^{\frac{x}{2}}dx
integral of (x^2+1)/(x^2+x-2)	\int\:\frac{x^{2}+1}{x^{2}+x-2}dx
y^'(t)=(y+1)(y-3),y(0)=1	y^{\prime\:}(t)=(y+1)(y-3),y(0)=1
t^3(dy)/(dt)+3t^2y=7cos(t),y(pi)=0	t^{3}\frac{dy}{dt}+3t^{2}y=7\cos(t),y(π)=0
limit as x approaches infinity of-x/s	\lim\:_{x\to\:\infty\:}(-\frac{x}{s})
derivative of 18(2e^{x^2}x^2+e^{x^2})	derivative\:18(2e^{x^{2}}x^{2}+e^{x^{2}})
longdivision (x-3)/(x+2)	longdivision\:\frac{x-3}{x+2}
derivative of 3^{2x^2}	\frac{d}{dx}(3^{2x^{2}})
(\partial)/(\partial x)(e^{7x^2+5y^2})	\frac{\partial\:}{\partial\:x}(e^{7x^{2}+5y^{2}})
tangent of f(x)=4x^2-2x+1	tangent\:f(x)=4x^{2}-2x+1
tangent of f(x)=sqrt(2x+1),\at x=3	tangent\:f(x)=\sqrt{2x+1},\at\:x=3
slope ofintercept (-1,-1),(1,5)	slopeintercept\:(-1,-1),(1,5)
derivative of (3x-1^4(2x+1)^{-3})	\frac{d}{dx}((3x-1)^{4}(2x+1)^{-3})
xy^'-y=x^2+5x-1	xy^{\prime\:}-y=x^{2}+5x-1
tangent of f(x)=3x^5-2x^4,\at x=4	tangent\:f(x)=3x^{5}-2x^{4},\at\:x=4
integral of 16sin^2(x)cos^3(x)	\int\:16\sin^{2}(x)\cos^{3}(x)dx
tangent of 1/(4x+3)	tangent\:\frac{1}{4x+3}
(\partial)/(\partial x)(7x-3y+4)	\frac{\partial\:}{\partial\:x}(7x-3y+4)
integral from 0 to 1 of x^6-x	\int\:_{0}^{1}x^{6}-xdx
y^'+ycos(x)=sin(x)cos(x)	y^{\prime\:}+y\cdot\:\cos(x)=\sin(x)\cdot\:\cos(x)
derivative of 3\sqrt[3]{x^2}	derivative\:3\sqrt[3]{x^{2}}
integral of (e^x+sec^2(x))/(e^x+tan(x))	\int\:\frac{e^{x}+\sec^{2}(x)}{e^{x}+\tan(x)}dx
inverse oflaplace (s-4)/((s^2+5)^2)	inverselaplace\:\frac{s-4}{(s^{2}+5)^{2}}
integral from 0 to 4 of xsqrt(x^2+9)	\int\:_{0}^{4}x\sqrt{x^{2}+9}dx
integral of 1/(x^4sqrt(x^2+3))	\int\:\frac{1}{x^{4}\sqrt{x^{2}+3}}dx
limit as x approaches 0 of (x^3)/(x^4)	\lim\:_{x\to\:0}(\frac{x^{3}}{x^{4}})
normal of y=5x^2,(-2,20)	normal\:y=5x^{2},(-2,20)
derivative of {f}(x(x^2))	\frac{d}{dx}({f}(x)(x^{2}))
integral of (5-50x)/(sqrt(1-25x^2))	\int\:\frac{5-50x}{\sqrt{1-25x^{2}}}dx
sum from n=0 to infinity of 2*6^n	\sum\:_{n=0}^{\infty\:}2\cdot\:6^{n}
(dy)/(dx)=((x-4))/(y+5)	\frac{dy}{dx}=\frac{(x-4)}{y+5}
derivative of (sqrt(t))/(2t+3)	derivative\:\frac{\sqrt{t}}{2t+3}
integral of cos^3(4θ)sin(4θ)	\int\:\cos^{3}(4θ)\sin(4θ)dθ
(dy)/(dx)=-xe^{-x+y}	\frac{dy}{dx}=-xe^{-x+y}
y^'=y(2+y)t	y^{\prime\:}=y(2+y)t
integral of 1/(xsqrt(x^2+1))	\int\:\frac{1}{x\sqrt{x^{2}+1}}dx
integral from 0 to 1 of (1/(1+x^2))	\int\:_{0}^{1}(\frac{1}{1+x^{2}})dx
limit as x approaches 6 of 4	\lim\:_{x\to\:6}(4)
integral of 3x^2sqrt(x^3)+1	\int\:3x^{2}\sqrt{x^{3}}+1dx
integral of (9x^3)/(sqrt(1+x^2))	\int\:\frac{9x^{3}}{\sqrt{1+x^{2}}}dx
derivative of e^{-2x}*cos(x)	\frac{d}{dx}(e^{-2x}\cdot\:\cos(x))
limit as x approaches 0+of 3x^{(x/2)}	\lim\:_{x\to\:0+}(3x^{(\frac{x}{2})})
integral of (2x+1)/((x+1)^3(x^2+4)^2)	\int\:\frac{2x+1}{(x+1)^{3}(x^{2}+4)^{2}}dx
integral of x-8	\int\:x-8dx
limit as x approaches 4 of ((x-5))/(x-4)	\lim\:_{x\to\:4}(\frac{(x-5)}{x-4})
integral of 3sin^3(x)cos^2(x)	\int\:3\sin^{3}(x)\cos^{2}(x)dx
integral of 2cos^3(t)	\int\:2\cos^{3}(t)dt
ty^'-3y=t^4	ty^{\prime\:}-3y=t^{4}
integral of x/(sqrt(3-x^2))	\int\:\frac{x}{\sqrt{3-x^{2}}}dx
integral of (x^2-2x+6)/((x+1)(x-2)^2)	\int\:\frac{x^{2}-2x+6}{(x+1)(x-2)^{2}}dx
derivative of x^2(120-x)	derivative\:x^{2}(120-x)
integral of 10sec^2(5x)tan(5x)	\int\:10\sec^{2}(5x)\tan(5x)dx
limit as x approaches pi/2 of xcos(x)	\lim\:_{x\to\:\frac{π}{2}}(x\cos(x))
integral of (x-3)^2e^{-x}	\int\:(x-3)^{2}e^{-x}dx
integral of e^{8x}	\int\:e^{8x}dx
(dQ)/(dt)=14.5-(7Q)/(800-2t)	\frac{dQ}{dt}=14.5-\frac{7Q}{800-2t}
limit as x approaches-4 of (x^2-3)/(4-x)	\lim\:_{x\to\:-4}(\frac{x^{2}-3}{4-x})
tangent of 2x^3-x^2+1	tangent\:2x^{3}-x^{2}+1
y^{''}-16y^'+289y=4t-21cos(17t)	y^{\prime\:\prime\:}-16y^{\prime\:}+289y=4t-21\cos(17t)
sum from n=1 to infinity of n2^n	\sum\:_{n=1}^{\infty\:}n2^{n}
integral of 1/(e^{-x)}	\int\:\frac{1}{e^{-x}}dx
integral of 2/5-5/x	\int\:\frac{2}{5}-\frac{5}{x}dx
integral of 1/((11-10x-x^2)^2)	\int\:\frac{1}{(11-10x-x^{2})^{2}}dx
derivative of 5/(sqrt(x+3))	\frac{d}{dx}(\frac{5}{\sqrt{x+3}})
limit as x approaches+0 of (1-2x)^{1/2}	\lim\:_{x\to\:+0}((1-2x)^{\frac{1}{2}})
f(x)=(sin(x))^{2x}	f(x)=(\sin(x))^{2x}
integral of (3x+1)/(x^2+4x+3)	\int\:\frac{3x+1}{x^{2}+4x+3}dx
integral of sqrt(tan(x))sec^4(x)	\int\:\sqrt{\tan(x)}\sec^{4}(x)dx
integral from 5 to 1 of-4x+1	\int\:_{5}^{1}-4x+1dx
sum from n=0 to infinity of-2-8-32-128	\sum\:_{n=0}^{\infty\:}-2-8-32-128
limit as x approaches 3 of (x^2+5)/(x+5)	\lim\:_{x\to\:3}(\frac{x^{2}+5}{x+5})
derivative of ln(x^2-3x+1)	\frac{d}{dx}(\ln(x^{2}-3x+1))
tangent of y=x^2-1,(-3,8)	tangent\:y=x^{2}-1,(-3,8)
(\partial)/(\partial x)(6x-5y)	\frac{\partial\:}{\partial\:x}(6x-5y)
sum from n=1 to infinity}(-1)^n(\sqrt{n of)/(n+2)	\sum\:_{n=1}^{\infty\:}(-1)^{n}\frac{\sqrt{n}}{n+2}
integral of (sqrt(289-x^2))/x	\int\:\frac{\sqrt{289-x^{2}}}{x}dx
limit as x approaches 0 of (1+x)^{5/x}	\lim\:_{x\to\:0}((1+x)^{\frac{5}{x}})
x^2(dy)/(dx)-2xy=6y^4,y(1)= 1/2	x^{2}\frac{dy}{dx}-2xy=6y^{4},y(1)=\frac{1}{2}
tangent of f(x)=sqrt(x^2+33),\at x=4	tangent\:f(x)=\sqrt{x^{2}+33},\at\:x=4
(\partial)/(\partial x)(2x+4y^2)	\frac{\partial\:}{\partial\:x}(2x+4y^{2})
integral of (x+1)(x-1)	\int\:(x+1)(x-1)dx
integral of (x^2-5x+1)/(3x^2)	\int\:\frac{x^{2}-5x+1}{3x^{2}}dx
(\partial)/(\partial x)(2sin(5x)cos(4y))	\frac{\partial\:}{\partial\:x}(2\sin(5x)\cos(4y))
integral of sin^2(t)cos^2(t)	\int\:\sin^{2}(t)\cos^{2}(t)dt
derivative of x^{6cos(x})	\frac{d}{dx}(x^{6\cos(x)})
tangent of 2/(1+x^2)	tangent\:\frac{2}{1+x^{2}}
y^'+y=e^{3x}	y^{\prime\:}+y=e^{3x}
derivative of 3^{x-1}	\frac{d}{dx}(3^{x-1})
integral of 1/(csc^4(3x)sec^2(3x))	\int\:\frac{1}{\csc^{4}(3x)\sec^{2}(3x)}dx

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