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Popular Calculus Problems

inverse oflaplace 1/((s+2)(s^2-2s+5))	inverselaplace\:\frac{1}{(s+2)(s^{2}-2s+5)}
integral from-3 to-1 of x^2e^{x^3+27}	\int\:_{-3}^{-1}x^{2}e^{x^{3}+27}dx
integral of tan^2(ax)cos(ax)	\int\:\tan^{2}(ax)\cos(ax)dx
integral of e^xarctan(e^x)	\int\:e^{x}\arctan(e^{x})dx
tangent of x^2+8x	tangent\:x^{2}+8x
integral of 7e^{5x+e^{5x}}	\int\:7e^{5x+e^{5x}}dx
integral of (x+1)e^{4x^2+8x}	\int\:(x+1)e^{4x^{2}+8x}dx
integral of [((x^2+10x+25))/((x+5))]	\int\:[\frac{(x^{2}+10x+25)}{(x+5)}]dx
integral of (e^x)/(1+81e^{2x)}	\int\:\frac{e^{x}}{1+81e^{2x}}dx
f(x)=1+sin(x)	f(x)=1+\sin(x)
(dy)/(dx)=(x^2+y^2)/(xy)	\frac{dy}{dx}=\frac{x^{2}+y^{2}}{xy}
derivative of 9x^2	derivative\:9x^{2}
maclaurin f(x)= x/2 (1+(x/2)^2)^{-1/2}	maclaurin\:f(x)=\frac{x}{2}(1+(\frac{x}{2})^{2})^{-\frac{1}{2}}
roots ax^2+bx+c	roots\:ax^{2}+bx+c
(dy)/(dx)+x/y =0	\frac{dy}{dx}+\frac{x}{y}=0
xy^'+2y=(3e^{-3x})/x	xy^{\prime\:}+2y=\frac{3e^{-3x}}{x}
(\partial)/(\partial x)(y^2-x^2-10)	\frac{\partial\:}{\partial\:x}(y^{2}-x^{2}-10)
(tdy)/(dt)=t^3+23t^3y	\frac{tdy}{dt}=t^{3}+23t^{3}y
derivative of ((6x^2-5)(x^2-6))/(x^2+4)	derivative\:\frac{(6x^{2}-5)(x^{2}-6)}{x^{2}+4}
y^{''}-(2sqrt(3))/3 y^'+2/9 =0	y^{\prime\:\prime\:}-\frac{2\sqrt{3}}{3}y^{\prime\:}+\frac{2}{9}=0
integral from 0 to 2 of (2x-1)^2	\int\:_{0}^{2}(2x-1)^{2}dx
integral of sec(3t)tan(3t)	\int\:\sec(3t)\tan(3t)dt
y^{''}+5y^'+10y=510e^{2t}cos(6t)	y^{\prime\:\prime\:}+5y^{\prime\:}+10y=510e^{2t}\cos(6t)
integral of (x^2)/(sqrt(6x-x^2))	\int\:\frac{x^{2}}{\sqrt{6x-x^{2}}}dx
y^'+xy=e^xy	y^{\prime\:}+xy=e^{x}y
integral of (8t^3+10)/(4t^2-4t+5)	\int\:\frac{8t^{3}+10}{4t^{2}-4t+5}dt
integral of x^4+1	\int\:x^{4}+1dx
integral of (3x+2)/(sqrt(19-5x+x^2))	\int\:\frac{3x+2}{\sqrt{19-5x+x^{2}}}dx
limit as x approaches c of 2.5(-2)	\lim\:_{x\to\:c}(2.5(-2))
integral of x^2(2x-5)	\int\:x^{2}(2x-5)dx
derivative of Q(x)=x^4+8x^2+16	derivative\:Q(x)=x^{4}+8x^{2}+16
integral of x^2e^{1-x}	\int\:x^{2}e^{1-x}dx
limit as x approaches+(-2) of (2x)/(x+2)	\lim\:_{x\to\:+(-2)}(\frac{2x}{x+2})
integral of 1/(sqrt(49+x^2))	\int\:\frac{1}{\sqrt{49+x^{2}}}dx
(\partial)/(\partial x)(x^3y^2-2x^2y+3x)	\frac{\partial\:}{\partial\:x}(x^{3}y^{2}-2x^{2}y+3x)
derivative of 3sin(2)	\frac{d}{dx}(3\sin(2))
derivative of g(x)= 1/(5x^2+2x)	derivative\:g(x)=\frac{1}{5x^{2}+2x}
y^{''}+5y^'+6.25y=0	y^{\prime\:\prime\:}+5y^{\prime\:}+6.25y=0
derivative of 5x-2x^2	\frac{d}{dx}(5x-2x^{2})
integral from 1 to 4 of x^{1/2}ln(x)	\int\:_{1}^{4}x^{\frac{1}{2}}\ln(x)dx
inverse oflaplace 1/(s+40)	inverselaplace\:\frac{1}{s+40}
integral of 1/(2x+7)	\int\:\frac{1}{2x+7}dx
integral from 0 to infinity of e^{-9x}	\int\:_{0}^{\infty\:}e^{-9x}dx
derivative of ((t^3)/(t^6+5))^2	derivative\:(\frac{t^{3}}{t^{6}+5})^{2}
derivative of (e^{2x}/(1+sin(pix)))	\frac{d}{dx}(\frac{e^{2x}}{1+\sin(πx)})
limit as x approaches 3-of-1/(x-3)	\lim\:_{x\to\:3-}(-\frac{1}{x-3})
integral from 1 to 3 of (x^2+1)	\int\:_{1}^{3}(x^{2}+1)dx
y^{''}+3y^'=6e^{-3t},y(0)=8,y^'(0)=-4	y^{\prime\:\prime\:}+3y^{\prime\:}=6e^{-3t},y(0)=8,y^{\prime\:}(0)=-4
derivative of e^xx^3+6e^xx^2+6e^xx	\frac{d}{dx}(e^{x}x^{3}+6e^{x}x^{2}+6e^{x}x)
y^2dx-(1-x)dy=0	y^{2}dx-(1-x)dy=0
limit as x approaches 0 of 3	\lim\:_{x\to\:0}(3)
derivative of-3x^5+4x^{-3}-5x^{-2}+5	\frac{d}{dx}(-3x^{5}+4x^{-3}-5x^{-2}+5)
limit as x approaches infinity of x/(2a)	\lim\:_{x\to\:\infty\:}(\frac{x}{2a})
(\partial)/(\partial x)(x/(R(x)))	\frac{\partial\:}{\partial\:x}(\frac{x}{R(x)})
sum from n=2 to infinity of 3/(7^n)	\sum\:_{n=2}^{\infty\:}\frac{3}{7^{n}}
inverse oflaplace s/(10(s^2+10s+9.8))	inverselaplace\:\frac{s}{10(s^{2}+10s+9.8)}
derivative of (sqrt(x)^3)	\frac{d}{dx}((\sqrt{x})^{3})
integral of x^7sqrt(x^4+7)	\int\:x^{7}\sqrt{x^{4}+7}dx
derivative of (4x+4)/(3x^{2/3)}	derivative\:\frac{4x+4}{3x^{\frac{2}{3}}}
derivative of cos^6(3x^2+4)	\frac{d}{dx}(\cos^{6}(3x^{2}+4))
laplacetransform 3sin(sqrt(2))	laplacetransform\:3\sin(\sqrt{2})
slope of 3x^3+5y^3=1	slope\:3x^{3}+5y^{3}=1
y^'-e^{7x+y}=0	y^{\prime\:}-e^{7x+y}=0
derivative of 3x^3+cos(x)	\frac{d}{dx}(3x^{3}+\cos(x))
limit as x approaches 2 of 3x+a	\lim\:_{x\to\:2}(3x+a)
area x^2,25,0,5	area\:x^{2},25,0,5
integral of x^2+4	\int\:x^{2}+4dx
derivative of (x-a(x-b)(x-c))	\frac{d}{dx}((x-a)(x-b)(x-c))
(dy)/(dt)+(4y)/(200+3t)=8	\frac{dy}{dt}+\frac{4y}{200+3t}=8
f(x)=2sec^2(x)tan(x)	f(x)=2\sec^{2}(x)\tan(x)
integral of (21)/((x^2-1)^2)	\int\:\frac{21}{(x^{2}-1)^{2}}dx
d/(dt)(e^{-2t}{y}(t))	\frac{d}{dt}(e^{-2t}{y}(t))
derivative of 2sin(2x)	derivative\:2\sin(2x)
derivative of f(x)=sqrt(3x+7)	derivative\:f(x)=\sqrt{3x+7}
integral of 2x^2+4	\int\:2x^{2}+4dx
area y=x^2-4x,y=3x	area\:y=x^{2}-4x,y=3x
derivative of f(x)=(20000)/(2+123e^{-0.1(x))}	derivative\:f(x)=\frac{20000}{2+123e^{-0.1(x)}}
limit as x approaches 7+of x	\lim\:_{x\to\:7+}(x)
integral from-2 to 3 of (13)/(x^4)	\int\:_{-2}^{3}\frac{13}{x^{4}}dx
derivative of sin(cos(2x-5))	\frac{d}{dx}(\sin(\cos(2x-5)))
integral of (xarcsin(x))/(sqrt(1-x^2))	\int\:\frac{x\arcsin(x)}{\sqrt{1-x^{2}}}dx
integral of x^i	\int\:x^{i}dx
integral of ((x+2))/(x+1)	\int\:\frac{(x+2)}{x+1}dx
limit as x approaches 1 of (x-1)/(x^2+1)	\lim\:_{x\to\:1}(\frac{x-1}{x^{2}+1})
integral of sqrt(6x+3)	\int\:\sqrt{6x+3}dx
sum from n=1 to infinity of 1/(e^{n^3)}	\sum\:_{n=1}^{\infty\:}\frac{1}{e^{n^{3}}}
integral of 1/((2x-1)^3)	\int\:\frac{1}{(2x-1)^{3}}dx
limit as x approaches-6 of (x^2+6)/(x-6)	\lim\:_{x\to\:-6}(\frac{x^{2}+6}{x-6})
derivative of e^{2-3x}	\frac{d}{dx}(e^{2-3x})
derivative of 3cosh(x)	\frac{d}{dx}(3\cosh(x))
derivative of sin^{-3}(x)	\frac{d}{dx}(\sin^{-3}(x))
derivative of (1+8x^2(x-x^2))	\frac{d}{dx}((1+8x^{2})(x-x^{2}))
derivative of x+3y	\frac{d}{dx}(x+3y)
integral of ((x^5+x^2-x+5)/x)	\int\:(\frac{x^{5}+x^{2}-x+5}{x})dx
slope of (2,-4),(5,8)	slope\:(2,-4),(5,8)
(\partial)/(\partial y)(x^2-xy+9y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-xy+9y^{2})
derivative of xsin(6/x)	derivative\:x\sin(\frac{6}{x})
(\partial)/(\partial x)(9e^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(9e^{\sqrt{xy}})
derivative of (e^{sqrt(ln(x)})^{2^{-x}})	\frac{d}{dx}((e^{\sqrt{\ln(x)}})^{2^{-x}})
integral of (12)/(x^2-1)	\int\:\frac{12}{x^{2}-1}dx

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