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Popular Calculus Problems

limit as x approaches x/2 of sin(x)	\lim\:_{x\to\:\frac{x}{2}}(\sin(x))
integral of-sin(x)*cos(x)	\int\:-\sin(x)\cdot\:\cos(x)dx
derivative of 2/((x^2-3x^2))	\frac{d}{dx}(\frac{2}{(x^{2}-3x)^{2}})
derivative of (x^2+a^2^5)	\frac{d}{dx}((x^{2}+a^{2})^{5})
(\partial)/(\partial x)(2x-5y+3)	\frac{\partial\:}{\partial\:x}(2x-5y+3)
derivative of 6e^{-4x}ln(x)	\frac{d}{dx}(6e^{-4x}\ln(x))
sum from n=1 to infinity of (7/6)^n	\sum\:_{n=1}^{\infty\:}(\frac{7}{6})^{n}
xy-2y+xy^'-y^'=0	xy-2y+xy^{\prime\:}-y^{\prime\:}=0
slope of (4,-1),(-9,-10)	slope\:(4,-1),(-9,-10)
derivative of sin^3(x^2)	derivative\:\sin^{3}(x^{2})
derivative of 1/(2(x+1^{1/2)})	\frac{d}{dx}(\frac{1}{2(x+1)^{\frac{1}{2}}})
limit as x approaches 49 of x^{3/2}	\lim\:_{x\to\:49}(x^{\frac{3}{2}})
integral of (x^4)/4-(x^3)/3+5x	\int\:\frac{x^{4}}{4}-\frac{x^{3}}{3}+5xdx
derivative of x^-	\frac{d}{dx}(x^{-})
inverse oflaplace (4s)/(4s^2+1)	inverselaplace\:\frac{4s}{4s^{2}+1}
derivative of sin((pix/6))	\frac{d}{dx}(\sin(\frac{πx}{6}))
derivative of y=x^2e^x	derivative\:y=x^{2}e^{x}
integral of (y^4+2y^2-1)/(sqrt(y))	\int\:\frac{y^{4}+2y^{2}-1}{\sqrt{y}}dy
tangent of y=5-7x^2,(-3,-58)	tangent\:y=5-7x^{2},(-3,-58)
integral of te^{3t}-e^t	\int\:te^{3t}-e^{t}dt
integral of 1/(sqrt(x^2-12))	\int\:\frac{1}{\sqrt{x^{2}-12}}dx
integral of 1/(xsqrt(25x^2-25))	\int\:\frac{1}{x\sqrt{25x^{2}-25}}dx
limit as x approaches-5.8 of ln(x^2-9)	\lim\:_{x\to\:-5.8}(\ln(x^{2}-9))
sum from n=1 to infinity of (n^2)/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{n^{3}}
derivative of 1/4 x	derivative\:\frac{1}{4}x
(e^tcos(t))^'	(e^{t}\cos(t))^{\prime\:}
(\partial)/(\partial y)(y^2-x)	\frac{\partial\:}{\partial\:y}(y^{2}-x)
(\partial)/(\partial z)(x+y)	\frac{\partial\:}{\partial\:z}(x+y)
integral of ((6x^2-3x)/(4x^3))	\int\:(\frac{6x^{2}-3x}{4x^{3}})dx
derivative of 2(8^x)	derivative\:2(8^{x})
y^{''}+21y=0	y^{\prime\:\prime\:}+21y=0
integral of x^2((x^3)/(12)+4)^3	\int\:x^{2}(\frac{x^{3}}{12}+4)^{3}dx
limit as x approaches infinity of (1+(sqrt(n)+3)/(4n+1))^{2sqrt(n)}	\lim\:_{x\to\:\infty\:}((1+\frac{\sqrt{n}+3}{4n+1})^{2\sqrt{n}})
integral of θ(θ-2)^3	\int\:θ(θ-2)^{3}dθ
integral of (9+3x)/(1+x^2)	\int\:\frac{9+3x}{1+x^{2}}dx
integral from 0 to pi/2 of-4cos^5(x)	\int\:_{0}^{\frac{π}{2}}-4\cos^{5}(x)dx
derivative of csc(3x+2)	\frac{d}{dx}(\csc(3x+2))
integral of cot(35x)	\int\:\cot(35x)dx
limit as x approaches infinity of 4x-x^3	\lim\:_{x\to\:\infty\:}(4x-x^{3})
derivative of f(x)= 4/(1-2x^2)	derivative\:f(x)=\frac{4}{1-2x^{2}}
integral of (e^{-5x})/x	\int\:\frac{e^{-5x}}{x}dx
integral from 1 to 100 of (33)/(x^3)	\int\:_{1}^{100}\frac{33}{x^{3}}dx
y^{''''}+6y^{''}+9y=0	y^{\prime\:\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}+9y=0
dy-(y/x+x/y)dx=0	dy-(\frac{y}{x}+\frac{x}{y})dx=0
integral of (sin(ln(2x)))/x	\int\:\frac{\sin(\ln(2x))}{x}dx
integral of x^{-2}	\int\:x^{-2}dx
derivative of f(x)=6e^x+4/(\sqrt[3]{x)}	derivative\:f(x)=6e^{x}+\frac{4}{\sqrt[3]{x}}
(\partial)/(\partial x)(5x^2-3xy^2+xyz)	\frac{\partial\:}{\partial\:x}(5x^{2}-3xy^{2}+xyz)
integral of-1/(1+u^2)	\int\:-\frac{1}{1+u^{2}}du
inverse oflaplace 3e^{-3s}	inverselaplace\:3e^{-3s}
x^2y^'+2xy=19cos^2(x)	x^{2}y^{\prime\:}+2xy=19\cos^{2}(x)
y^{''}+8y^'-9y=0,y(1)=1,y^'(1)=0	y^{\prime\:\prime\:}+8y^{\prime\:}-9y=0,y(1)=1,y^{\prime\:}(1)=0
integral of rsqrt(16-r^2)	\int\:r\sqrt{16-r^{2}}dr
integral from 0 to 2 of (3x^2+2)	\int\:_{0}^{2}(3x^{2}+2)dx
integral of ((x+2))/(x^2-1)	\int\:\frac{(x+2)}{x^{2}-1}dx
integral of (1-cos(x))^3	\int\:(1-\cos(x))^{3}dx
limit as x approaches-4 of-x^2+2x-3	\lim\:_{x\to\:-4}(-x^{2}+2x-3)
integral of e^{2x}arctan(e^x)	\int\:e^{2x}\arctan(e^{x})dx
derivative of arccos(5x)	derivative\:\arccos(5x)
derivative of x^4(x-2^3)	\frac{d}{dx}(x^{4}(x-2)^{3})
y^{''}-4y^'+3y=7x^3e^{(2x)}cos(2x)	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=7x^{3}e^{(2x)}\cos(2x)
limit as x approaches 0 of 1/(e^x+1)	\lim\:_{x\to\:0}(\frac{1}{e^{x}+1})
integral of (sin^3(x))/(cos^7(x))	\int\:\frac{\sin^{3}(x)}{\cos^{7}(x)}dx
derivative of 4/3 pix^3	\frac{d}{dx}(\frac{4}{3}πx^{3})
integral from 1 to 100 of (37)/(x^3)	\int\:_{1}^{100}\frac{37}{x^{3}}dx
derivative of (3+x^2^{-1})	\frac{d}{dx}((3+x^{2})^{-1})
derivative of f(x)=sqrt(4x+3)	derivative\:f(x)=\sqrt{4x+3}
taylor x-pi/2 ,1	taylor\:x-\frac{π}{2},1
limit as t approaches 0 of tan(5t)	\lim\:_{t\to\:0}(\tan(5t))
derivative of (2x-3/(3x+4))	\frac{d}{dx}(\frac{2x-3}{3x+4})
integral of 2/(x^6)	\int\:\frac{2}{x^{6}}dx
derivative of x^2+64	derivative\:x^{2}+64
(\partial)/(\partial x)(9e^{xy+8})	\frac{\partial\:}{\partial\:x}(9e^{xy+8})
area x=y^2-10,x=3y	area\:x=y^{2}-10,x=3y
derivative of cy^{-2}	derivative\:cy^{-2}
sum from n=0 to infinity of 1/(2+6^{-n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2+6^{-n}}
derivative of 1/(sqrt(25-x^2))	\frac{d}{dx}(\frac{1}{\sqrt{25-x^{2}}})
integral of sin^6(t)*cos^3(t)	\int\:\sin^{6}(t)\cdot\:\cos^{3}(t)dt
integral of 2/(3x+2)	\int\:\frac{2}{3x+2}dx
slope of (-17,60),(37,-20)	slope\:(-17,60),(37,-20)
integral of x^2e^{kx}	\int\:x^{2}e^{kx}dx
derivative of y=(x+1/x)^{-1}	derivative\:y=(x+\frac{1}{x})^{-1}
integral of (cos(t))/(4+sin(t))	\int\:\frac{\cos(t)}{4+\sin(t)}dt
derivative of g(x)=3(4-9x)^4	derivative\:g(x)=3(4-9x)^{4}
integral of (2e^x)/(e^{2x)+8e^x+16}	\int\:\frac{2e^{x}}{e^{2x}+8e^{x}+16}dx
limit as x approaches-3+of 1/(x+3)	\lim\:_{x\to\:-3+}(\frac{1}{x+3})
tangent of f(x)=-x^3+4x^2,\at x=3	tangent\:f(x)=-x^{3}+4x^{2},\at\:x=3
area y=x^3-2x^2+3,y=3x^2+5x-22	area\:y=x^{3}-2x^{2}+3,y=3x^{2}+5x-22
area y=x^{15/14},y=13x^{1/14}	area\:y=x^{\frac{15}{14}},y=13x^{\frac{1}{14}}
derivative of \sqrt[9]{t}-9e^t	derivative\:\sqrt[9]{t}-9e^{t}
derivative of x^3+3x	\frac{d}{dx}(x^{3}+3x)
derivative of (1/(x^2-9/(x^4))(x+3x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{9}{x^{4}})(x+3x^{3}))
integral from-2 to 2 of 4-x^2	\int\:_{-2}^{2}4-x^{2}dx
integral from 0 to 3 of 4-x	\int\:_{0}^{3}4-xdx
(dy)/(dx)=(xe^{2x})/(x+k)	\frac{dy}{dx}=\frac{xe^{2x}}{x+k}
y^{''}+2y^'+14y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+14y=0,y(0)=1,y^{\prime\:}(0)=0
integral of x^2sqrt(3x+5)	\int\:x^{2}\sqrt{3x+5}dx
f(x)=sin(3x+2)	f(x)=\sin(3x+2)
integral from 1 to 5 of 2sqrt(x-1)	\int\:_{1}^{5}2\sqrt{x-1}dx
integral of 1/(4+x)	\int\:\frac{1}{4+x}dx

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