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Popular Calculus Problems

integral of xy+1	\int\:xy+1dy
inverse oflaplace 1/((t+1)^2)	inverselaplace\:\frac{1}{(t+1)^{2}}
integral of (x+4)/(2x+3)	\int\:\frac{x+4}{2x+3}dx
y^{''}+y=e^xsin(x)	y^{\prime\:\prime\:}+y=e^{x}\sin(x)
integral of (sqrt(2x))/x	\int\:\frac{\sqrt{2x}}{x}dx
integral of 1+2cos(x)+cos^2(x)	\int\:1+2\cos(x)+\cos^{2}(x)dx
area y=x^3,y=x^2	area\:y=x^{3},y=x^{2}
(\partial)/(\partial t)(t^2+1)	\frac{\partial\:}{\partial\:t}(t^{2}+1)
tangent of f(x)=((x^2))/(x-5)	tangent\:f(x)=\frac{(x^{2})}{x-5}
limit as x approaches 0 of (x(x-1))/x	\lim\:_{x\to\:0}(\frac{x(x-1)}{x})
derivative of u/(u^2+4)	derivative\:\frac{u}{u^{2}+4}
laplacetransform e^{2(t-3)}(3t^4+2t^3+t)	laplacetransform\:e^{2(t-3)}(3t^{4}+2t^{3}+t)
(\partial)/(\partial y)(cos(x-y)-xe^y)	\frac{\partial\:}{\partial\:y}(\cos(x-y)-xe^{y})
tangent of x^2+xy+2y^2=16,(-2,-2)	tangent\:x^{2}+xy+2y^{2}=16,(-2,-2)
integral of (x^2-2x)(x^3-3x^2)^2	\int\:(x^{2}-2x)(x^{3}-3x^{2})^{2}dx
(\partial)/(\partial x)((5x+8y)^{11})	\frac{\partial\:}{\partial\:x}((5x+8y)^{11})
(d^2)/(dx^2)((x^2)/(5+x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{5+x})
integral from 3 to 6 of (2x-10)	\int\:_{3}^{6}(2x-10)dx
derivative of-128cos(2x)	\frac{d}{dx}(-128\cos(2x))
integral from 0 to pi of 7sin^2(2x)	\int\:_{0}^{π}7\sin^{2}(2x)dx
derivative of e^{-x}+1/(e^{8x})	\frac{d}{dx}(e^{-x}+\frac{1}{e^{8x}})
integral of sin(x)cos(cos(x))	\int\:\sin(x)\cos(\cos(x))dx
integral from 1 to x^2 of 1/t	\int\:_{1}^{x^{2}}\frac{1}{t}dt
integral of ((x^4-3x^2+5)/(x^4))	\int\:(\frac{x^{4}-3x^{2}+5}{x^{4}})dx
x^2(dy)/(dx)-x=1+y+xy	x^{2}\frac{dy}{dx}-x=1+y+xy
derivative of f(x)=12x	derivative\:f(x)=12x
integral of e^{x^2}2x	\int\:e^{x^{2}}2xdx
taylor 1/(1-x),9	taylor\:\frac{1}{1-x},9
derivative of 16sin(x)	\frac{d}{dx}(16\sin(x))
y^{''}+13y^'+26y=5446e^{2t}cos(14t)	y^{\prime\:\prime\:}+13y^{\prime\:}+26y=5446e^{2t}\cos(14t)
integral of (x^2-4)e^{2x}	\int\:(x^{2}-4)e^{2x}dx
derivative of (2x/(6x^2+1))	\frac{d}{dx}(\frac{2x}{6x^{2}+1})
(dy)/(dx)=xy+x	\frac{dy}{dx}=xy+x
derivative of x-3ln(x)	\frac{d}{dx}(x-3\ln(x))
derivative of e^{-xt}	\frac{d}{dx}(e^{-xt})
limit as x approaches 3+of ([x])/x	\lim\:_{x\to\:3+}(\frac{[x]}{x})
y^{''}-y=e^x	y^{\prime\:\prime\:}-y=e^{x}
integral of (6x+1)sqrt(2x-3)	\int\:(6x+1)\sqrt{2x-3}dx
integral of (x^2-3x+1)/((x-1)^3)	\int\:\frac{x^{2}-3x+1}{(x-1)^{3}}dx
f(x)=4x^2sin(4x)	f(x)=4x^{2}\sin(4x)
integral of (sqrt(x)+x^{1/3}+x)/(x^2)	\int\:\frac{\sqrt{x}+x^{\frac{1}{3}}+x}{x^{2}}dx
integral from 0 to 1 of e^{-2x}	\int\:_{0}^{1}e^{-2x}dx
area y=sqrt(x),x=4	area\:y=\sqrt{x},x=4
integral of tan^7(x)	\int\:\tan^{7}(x)dx
derivative of y=(x^5+1)^6	derivative\:y=(x^{5}+1)^{6}
derivative of y=4x^2+2	derivative\:y=4x^{2}+2
integral of sqrt(t^4+2t^2+1)	\int\:\sqrt{t^{4}+2t^{2}+1}dt
integral of 1/((1+x^2))	\int\:\frac{1}{(1+x^{2})}dx
derivative of 12^{9x}	derivative\:12^{9x}
limit as x approaches 2 of (x-2)/(\|x-2\|)	\lim\:_{x\to\:2}(\frac{x-2}{\left\|x-2\right\|})
integral of sin(2x)e^{(3x)}	\int\:\sin(2x)e^{(3x)}dx
limit as y approaches 0 of 0/(y^2)	\lim\:_{y\to\:0}(\frac{0}{y^{2}})
inverse oflaplace 1/((s+1)(s+3)^2)	inverselaplace\:\frac{1}{(s+1)(s+3)^{2}}
integral of (x^3+6x^2+2x+3)/(x^2+6x+1)	\int\:\frac{x^{3}+6x^{2}+2x+3}{x^{2}+6x+1}dx
integral of 5x\sqrt[3]{1-x^2}	\int\:5x\sqrt[3]{1-x^{2}}dx
integral of 1/(49e^{-7x)+e^{7x}}	\int\:\frac{1}{49e^{-7x}+e^{7x}}dx
(dy)/(dx)=e^{x^2}	\frac{dy}{dx}=e^{x^{2}}
derivative of (ln(x))^4	derivative\:(\ln(x))^{4}
2xy(dy)/(dx)+y^2=2x^2	2xy\frac{dy}{dx}+y^{2}=2x^{2}
derivative of ln(8x)	derivative\:\ln(8x)
sum from n=1 to infinity of n/(2n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n^{2}+1}
integral from 0 to 3 of xe^{-x}	\int\:_{0}^{3}xe^{-x}dx
derivative of A/(y^{12)}+Be^y	derivative\:\frac{A}{y^{12}}+Be^{y}
tangent of f(x)=x^2-6,(3,3)	tangent\:f(x)=x^{2}-6,(3,3)
derivative of xln(x^2+1)	\frac{d}{dx}(x\ln(x^{2}+1))
integral of (e^x)/((1+e^x))	\int\:\frac{e^{x}}{(1+e^{x})}dx
integral of (3+x)	\int\:(3+x)dx
integral of p(p+2)^6	\int\:p(p+2)^{6}dp
derivative of 1/(x^2-3/(x^4))	\frac{d}{dx}(\frac{1}{x^{2}}-\frac{3}{x^{4}})
area y=x^4,y=x	area\:y=x^{4},y=x
derivative of x^2(3x^4-7x+2)	\frac{d}{dx}(x^{2}(3x^{4}-7x+2))
derivative of (sec(x)/(4x^2+5))	\frac{d}{dx}(\frac{\sec(x)}{4x^{2}+5})
inverse oflaplace s/(s^2+4s+8)	inverselaplace\:\frac{s}{s^{2}+4s+8}
derivative of g(x)=-x^2+7x+7	derivative\:g(x)=-x^{2}+7x+7
y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+16y^{\prime\:}+65y=0,y(0)=1,y^{\prime\:}(0)=0
tangent of f(x)=8x^{1/3}-5,\at x=8	tangent\:f(x)=8x^{\frac{1}{3}}-5,\at\:x=8
3yy^'=x	3yy^{\prime\:}=x
d/(dt)(2^t-2t)	\frac{d}{dt}(2^{t}-2t)
d/(dy)(x+2y)	\frac{d}{dy}(x+2y)
inverse oflaplace s/((s^2+s+1))	inverselaplace\:\frac{s}{(s^{2}+s+1)}
limit as x approaches-3 of x^2+9x+4	\lim\:_{x\to\:-3}(x^{2}+9x+4)
integral from 3 to 5 of (5x^3+6)	\int\:_{3}^{5}(5x^{3}+6)dx
(y+2)dx+(x-2)dy=0	(y+2)dx+(x-2)dy=0
(dy)/(dx)=((x+1))/((x^2+2x-3)^2)	\frac{dy}{dx}=\frac{(x+1)}{(x^{2}+2x-3)^{2}}
limit as x approaches 9 of 12	\lim\:_{x\to\:9}(12)
integral of x^2(1+x^3)	\int\:x^{2}(1+x^{3})dx
integral of 4/3 t^3-4t^2+3t+10	\int\:\frac{4}{3}t^{3}-4t^{2}+3t+10dt
d/(dt)(t+1)	\frac{d}{dt}(t+1)
limit as x approaches 5+of 2/(x^2-25)	\lim\:_{x\to\:5+}(\frac{2}{x^{2}-25})
derivative of cos(a^8+x^8)	derivative\:\cos(a^{8}+x^{8})
limit as x approaches 0 of (sqrt(x+36)-6)/x	\lim\:_{x\to\:0}(\frac{\sqrt{x+36}-6}{x})
derivative of (-x^2)/(y^2)	derivative\:\frac{-x^{2}}{y^{2}}
derivative of-4x^2	derivative\:-4x^{2}
y^'=(3y-4x)/(2y-3x)	y^{\prime\:}=\frac{3y-4x}{2y-3x}
integral of sqrt(xy)	\int\:\sqrt{xy}dy
area y=3sqrt(x),x+y=4,y=1,y=0	area\:y=3\sqrt{x},x+y=4,y=1,y=0
integral of 3/(x^2+3)	\int\:\frac{3}{x^{2}+3}dx
(dy)/(dx)=x^4-1	\frac{dy}{dx}=x^{4}-1
derivative of g(x)=1+6x+3x^2	derivative\:g(x)=1+6x+3x^{2}
integral of x/(x^2+4x+20)	\int\:\frac{x}{x^{2}+4x+20}dx

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