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Popular Calculus Problems

integral of 1/(25+4x^2)	\int\:\frac{1}{25+4x^{2}}dx
integral of (sin(x)-4)/(cos(x))	\int\:\frac{\sin(x)-4}{\cos(x)}dx
integral of (sin^2(x))/x	\int\:\frac{\sin^{2}(x)}{x}dx
integral of e^{-2y}	\int\:e^{-2y}dy
derivative of 900x-1/3 x^3+2500	\frac{d}{dx}(900x-\frac{1}{3}x^{3}+2500)
integral of (-x+1)/(x^2+x+1)	\int\:\frac{-x+1}{x^{2}+x+1}dx
5y^{''}+5y^'-10y=0	5y^{\prime\:\prime\:}+5y^{\prime\:}-10y=0
integral from-infinity to 0 of (4-3x)e^x	\int\:_{-\infty\:}^{0}(4-3x)e^{x}dx
integral from 0 to 4 of 3/(x^2)	\int\:_{0}^{4}\frac{3}{x^{2}}dx
(d^2)/(dx^2)(5e^x)	\frac{d^{2}}{dx^{2}}(5e^{x})
tangent of f(x)=5x^2-4x+3	tangent\:f(x)=5x^{2}-4x+3
y^{''}=k^2*y	y^{\prime\:\prime\:}=k^{2}\cdot\:y
integral of 5e^{-x}	\int\:5e^{-x}dx
y^'-4xy=0	y^{\prime\:}-4xy=0
cos^2(x)sin(x)y^'+(cos^3(x))y=1	\cos^{2}(x)\sin(x)y^{\prime\:}+(\cos^{3}(x))y=1
derivative of (4x^2+5)(3x-2)	derivative\:(4x^{2}+5)(3x-2)
limit as x approaches 4 of (ax^3)/(x-4)	\lim\:_{x\to\:4}(\frac{ax^{3}}{x-4})
(dy)/(dx)=(xy)^{1/3},y(2)=1	\frac{dy}{dx}=(xy)^{\frac{1}{3}},y(2)=1
derivative of 7xe^{-9x}	\frac{d}{dx}(7xe^{-9x})
f(x)=-sin(2x)	f(x)=-\sin(2x)
limit as x approaches 0 of (3x^2)/(1-cos^2(x/2))	\lim\:_{x\to\:0}(\frac{3x^{2}}{1-\cos^{2}(\frac{x}{2})})
integral of (x^3+x^2+2)/(x^2-x)	\int\:\frac{x^{3}+x^{2}+2}{x^{2}-x}dx
integral of 1/((x^2+2x+3)^{3/2)}	\int\:\frac{1}{(x^{2}+2x+3)^{\frac{3}{2}}}dx
(dy)/(dx)=6yx	\frac{dy}{dx}=6yx
limit as x approaches 0 of 5/x	\lim\:_{x\to\:0}(\frac{5}{x})
(dy)/(dx)+5e^{x+y}=0	\frac{dy}{dx}+5e^{x+y}=0
integral from 1 to 2 of (2x^2)-(2x+6)	\int\:_{1}^{2}(2x^{2})-(2x+6)dx
tangent of (x^2-1)/(x^2+x+1)(1)	tangent\:\frac{x^{2}-1}{x^{2}+x+1}(1)
integral from-pi/4 to pi/4 of x^2	\int\:_{-\frac{π}{4}}^{\frac{π}{4}}x^{2}dx
integral of 1/(sqrt(9x^2-6x+5))	\int\:\frac{1}{\sqrt{9x^{2}-6x+5}}dx
integral from 1 to 8 of x/(x^2+4x+20)	\int\:_{1}^{8}\frac{x}{x^{2}+4x+20}dx
simplify x/(log_{e)(x)}	simplify\:\frac{x}{\log_{e}(x)}
integral of e^{x^2}*x	\int\:e^{x^{2}}\cdot\:xdx
(2y-2)(dy)/(dx)=3x^2+4x+2	(2y-2)\frac{dy}{dx}=3x^{2}+4x+2
(\partial)/(\partial x)(xy^2+x^2y)	\frac{\partial\:}{\partial\:x}(xy^{2}+x^{2}y)
tangent of y=(x^2-1)/(x^2+x+1)	tangent\:y=\frac{x^{2}-1}{x^{2}+x+1}
integral of (x^2+2x-1)/(x(x+2)(2x-1))	\int\:\frac{x^{2}+2x-1}{x(x+2)(2x-1)}dx
(\partial)/(\partial x)(-4cos(x))	\frac{\partial\:}{\partial\:x}(-4\cos(x))
limit as x approaches 1 of 4x-5	\lim\:_{x\to\:1}(4x-5)
(\partial)/(\partial z)(xye^{yz})	\frac{\partial\:}{\partial\:z}(xye^{yz})
integral of (2+2x)	\int\:(2+2x)dx
limit as x approaches 0 of (cos(1/x))/x	\lim\:_{x\to\:0}(\frac{\cos(\frac{1}{x})}{x})
integral of (cot(2t))^5	\int\:(\cot(2t))^{5}dt
derivative of f(x)=(5x-2)^2	derivative\:f(x)=(5x-2)^{2}
tangent of y=x^2-3,(5,22)	tangent\:y=x^{2}-3,(5,22)
integral of (x^5)/(e^{x^6)}	\int\:\frac{x^{5}}{e^{x^{6}}}dx
limit as x approaches 0 of (sin(3x))/(tan(10x))	\lim\:_{x\to\:0}(\frac{\sin(3x)}{\tan(10x)})
(d^2)/(dx^2)(x^{1/10})	\frac{d^{2}}{dx^{2}}(x^{\frac{1}{10}})
area y=2x+1,(1,5)	area\:y=2x+1,(1,5)
integral of cos(5x)x	\int\:\cos(5x)xdx
(\partial)/(\partial s)(ln(1+s^2+t^2))	\frac{\partial\:}{\partial\:s}(\ln(1+s^{2}+t^{2}))
limit as x approaches 3 of-5/8*x^4	\lim\:_{x\to\:3}(-\frac{5}{8}\cdot\:x^{4})
area y=x^2-6x,y=-x^2+4x	area\:y=x^{2}-6x,y=-x^{2}+4x
y^'=-50ky+k	y^{\prime\:}=-50ky+k
integral from 0 to 2 of-t^3	\int\:_{0}^{2}-t^{3}dt
integral of (2x^3+3x)/((x^4+3x^2+7)^4)	\int\:\frac{2x^{3}+3x}{(x^{4}+3x^{2}+7)^{4}}dx
integral from 1 to 2 of (1+2y)^2	\int\:_{1}^{2}(1+2y)^{2}dy
integral of 1/(x(x+a))	\int\:\frac{1}{x(x+a)}dx
integral of (32)/(1-cos(8x))	\int\:\frac{32}{1-\cos(8x)}dx
integral of 1/4 e^{2x}	\int\:\frac{1}{4}e^{2x}dx
(dy)/(dx)=e^{6x}+12y	\frac{dy}{dx}=e^{6x}+12y
derivative of (1/(2x+3))^3	derivative\:(\frac{1}{2x+3})^{3}
slope of (-1.2)(5.5)	slope\:(-1.2)(5.5)
derivative of sin((pix/(11)))	\frac{d}{dx}(\sin(\frac{πx}{11}))
integral of 6x^2sqrt(3x^3-1)	\int\:6x^{2}\sqrt{3x^{3}-1}dx
integral of (x+3)^2	\int\:(x+3)^{2}dx
integral from 0 to x of 3e^{-3x}	\int\:_{0}^{x}3e^{-3x}dx
limit as x approaches infinity of 13x	\lim\:_{x\to\:\infty\:}(13x)
integral of x^9sqrt(x^5+7)	\int\:x^{9}\sqrt{x^{5}+7}dx
derivative of (x^2-25)/(x-5)	derivative\:\frac{x^{2}-25}{x-5}
y^'=(y^2)/x	y^{\prime\:}=\frac{y^{2}}{x}
integral of x*sqrt(1-x)	\int\:x\cdot\:\sqrt{1-x}dx
xy^'-y=x^2-x+2	xy^{\prime\:}-y=x^{2}-x+2
limit as s approaches 5 of 5/((s-5)^2)	\lim\:_{s\to\:5}(\frac{5}{(s-5)^{2}})
derivative of sin(2^{sqrt(1+1/x)})	\frac{d}{dx}(\sin(2^{\sqrt{1+\frac{1}{x}}}))
integral of ((ln(x))^n)/x	\int\:\frac{(\ln(x))^{n}}{x}dx
integral of (cos(x))/(sqrt(2sin(x)))	\int\:\frac{\cos(x)}{\sqrt{2\sin(x)}}dx
limit as x approaches 0 of (1/(5x))-(1/(e^{5x)}-1)	\lim\:_{x\to\:0}((\frac{1}{5x})-(\frac{1}{e^{5x}}-1))
derivative of 3(5^x)	derivative\:3(5^{x})
integral from 0 to 2 of (2x-5)^2	\int\:_{0}^{2}(2x-5)^{2}dx
derivative of ((3x+2/(x-1))^7)	\frac{d}{dx}((\frac{3x+2}{x-1})^{7})
y^'=(3x^4+y^4)/(xy^3)	y^{\prime\:}=\frac{3x^{4}+y^{4}}{xy^{3}}
tangent of f(x)= 1/(5+3x),(-1, 1/2)	tangent\:f(x)=\frac{1}{5+3x},(-1,\frac{1}{2})
(\partial)/(\partial x)(yln(x^2+y^2+4))	\frac{\partial\:}{\partial\:x}(y\ln(x^{2}+y^{2}+4))
derivative of x^3-3/x+e^2	\frac{d}{dx}(x^{3}-\frac{3}{x}+e^{2})
integral of (cos^2(x)*sin(x))	\int\:(\cos^{2}(x)\cdot\:\sin(x))dx
integral of (12x^3)/(x^4+7)	\int\:\frac{12x^{3}}{x^{4}+7}dx
derivative of f(x)=(2x)/(sin(x)+cos(x))	derivative\:f(x)=\frac{2x}{\sin(x)+\cos(x)}
integral of ((y^2+1)^2)/(y^2)	\int\:\frac{(y^{2}+1)^{2}}{y^{2}}dy
limit as x approaches 2 of 3/x	\lim\:_{x\to\:2}(\frac{3}{x})
(\partial)/(\partial x)(3xe^y-x^3-e^{3y})	\frac{\partial\:}{\partial\:x}(3xe^{y}-x^{3}-e^{3y})
integral of 3x^2y+e^xsin(y)	\int\:3x^{2}y+e^{x}\sin(y)dx
y^'+((x-2))/(x-1)y=0	y^{\prime\:}+\frac{(x-2)}{x-1}y=0
derivative of x^2*ln(2x)	\frac{d}{dx}(x^{2}\cdot\:\ln(2x))
inverse oflaplace s/(s^2+25)	inverselaplace\:\frac{s}{s^{2}+25}
121y^{''}-16y=0	121y^{\prime\:\prime\:}-16y=0
(\partial)/(\partial x)((x+y)^2)	\frac{\partial\:}{\partial\:x}((x+y)^{2})
sum from n=1 to infinity of 1/(n^2+3n+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+3n+2}
integral of ((x+1))/((x^2+2x))	\int\:\frac{(x+1)}{(x^{2}+2x)}dx
integral of (6x^3-12x^2+8)/(x^2-2x)	\int\:\frac{6x^{3}-12x^{2}+8}{x^{2}-2x}dx

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