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Popular Calculus Problems

integral of 27tan^3(x)sec(x)	\int\:27\tan^{3}(x)\sec(x)dx
derivative of-5/(x^2+3)	derivative\:-\frac{5}{x^{2}+3}
integral of (x^4)/((1-x)^3)	\int\:\frac{x^{4}}{(1-x)^{3}}dx
derivative of f(x)=(x^4+3x)^{-1}	derivative\:f(x)=(x^{4}+3x)^{-1}
integral of sin^2(θ)tan(θ)	\int\:\sin^{2}(θ)\tan(θ)dθ
(\partial)/(\partial x)(e^x+y+y^2+6)	\frac{\partial\:}{\partial\:x}(e^{x}+y+y^{2}+6)
limit as x approaches 0 of ln(1-x)	\lim\:_{x\to\:0}(\ln(1-x))
integral of (cos^4(x))(sin(x))	\int\:(\cos^{4}(x))(\sin(x))dx
derivative of 5\sqrt[3]{x^2}	\frac{d}{dx}(5\sqrt[3]{x^{2}})
limit as x approaches-6 of 6x+1	\lim\:_{x\to\:-6}(6x+1)
(d^2)/(dx^2)((2x+3)/(3x-1))	\frac{d^{2}}{dx^{2}}(\frac{2x+3}{3x-1})
slope of (-8.1)(2.7)	slope\:(-8.1)(2.7)
derivative of ((e^x))/(5-x)	derivative\:\frac{(e^{x})}{5-x}
(1+xe^{2/x})^'	(1+xe^{\frac{2}{x}})^{\prime\:}
derivative of cos(5x-1)	\frac{d}{dx}(\cos(5x)-1)
integral of (1-cos(x))/(1+sin(x))	\int\:\frac{1-\cos(x)}{1+\sin(x)}dx
derivative of f(x)=(x^2)/((x-2)^2)	derivative\:f(x)=\frac{x^{2}}{(x-2)^{2}}
y^{''}+16y^'=0	y^{\prime\:\prime\:}+16y^{\prime\:}=0
integral of (sin^2(7t))	\int\:(\sin^{2}(7t))dt
derivative of 5^{ln(x})	\frac{d}{dx}(5^{\ln(x)})
integral of (-x)/(x^2+9)	\int\:\frac{-x}{x^{2}+9}dx
derivative of (6x^2+4x+6/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+4x+6}{\sqrt{x}})
derivative of (x^6/(3-x^5))	\frac{d}{dx}(\frac{x^{6}}{3-x^{5}})
derivative of 2x-cos^2(x+sqrt(2))	\frac{d}{dx}(2x-\cos^{2}(x)+\sqrt{2})
x^'+2x=5e^{3t}	x^{\prime\:}+2x=5e^{3t}
area x=y^2,x=y+2,y=0	area\:x=y^{2},x=y+2,y=0
integral of (2^x)/(1+2^x)	\int\:\frac{2^{x}}{1+2^{x}}dx
inverse oflaplace (36)/(s(s^2+1)(s^2+9))	inverselaplace\:\frac{36}{s(s^{2}+1)(s^{2}+9)}
integral of e^{-23x}	\int\:e^{-23x}dx
integral of (2y+x)/(1+x)	\int\:\frac{2y+x}{1+x}dx
derivative of y=(14x-x^2)^3	derivative\:y=(14x-x^{2})^{3}
sum from n=1 to infinity of n^{15}	\sum\:_{n=1}^{\infty\:}n^{15}
derivative of sqrt(x)(x^3-1)^6	derivative\:\sqrt{x}(x^{3}-1)^{6}
integral of 1/(x^2+8x+97)	\int\:\frac{1}{x^{2}+8x+97}dx
integral of e^{7x}cos(5x)	\int\:e^{7x}\cos(5x)dx
(\partial)/(\partial x)(ycos(4x))	\frac{\partial\:}{\partial\:x}(y\cos(4x))
d/(dt)(asin(γt)+bcos(γt))	\frac{d}{dt}(a\sin(γt)+b\cos(γt))
integral of (x^2+3x)^2(2x+3)	\int\:(x^{2}+3x)^{2}(2x+3)dx
integral of-4sin(-2t)	\int\:-4\sin(-2t)dt
integral of 3t^2(t^3+4)^5	\int\:3t^{2}(t^{3}+4)^{5}dt
taylor 1/(1+1/x),0	taylor\:\frac{1}{1+\frac{1}{x}},0
integral from-1 to 1 of (x-sqrt(1-x^2))	\int\:_{-1}^{1}(x-\sqrt{1-x^{2}})dx
ty^'=3y+t^4sin(4t)	ty^{\prime\:}=3y+t^{4}\sin(4t)
P^'=200e^{0.02t}	P^{\prime\:}=200e^{0.02t}
f(x)=sqrt(x+5)	f(x)=\sqrt{x+5}
integral of (x^2)/((x-2)^3)	\int\:\frac{x^{2}}{(x-2)^{3}}dx
(\partial)/(\partial x)(sqrt(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}-y^{2}})
area 6sin(x),6cos(2x),[-pi/2 , pi/6 ]	area\:6\sin(x),6\cos(2x),[-\frac{π}{2},\frac{π}{6}]
derivative of f(x)= 1/(sqrt(x+2))	derivative\:f(x)=\frac{1}{\sqrt{x+2}}
y^{''}-4y^'+4y=te^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=te^{2t}
derivative of x^{2/3}-3	\frac{d}{dx}(x^{\frac{2}{3}}-3)
integral of 1/(x(\sqrt[3]{x))}	\int\:\frac{1}{x(\sqrt[3]{x})}dx
integral of (4x)/(sqrt(x^2-9))	\int\:\frac{4x}{\sqrt{x^{2}-9}}dx
sum from n=1 to infinity of 3x^n	\sum\:_{n=1}^{\infty\:}3x^{n}
derivative of (4x^2-7x+5)/(2x+1)	derivative\:\frac{4x^{2}-7x+5}{2x+1}
integral of x^2-5x+4	\int\:x^{2}-5x+4dx
sum from n=0 to infinity of 1/(100^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{100^{n}}
limit as x approaches 2 of x^2+7x-5	\lim\:_{x\to\:2}(x^{2}+7x-5)
integral of (1+ln^3(x))/x	\int\:\frac{1+\ln^{3}(x)}{x}dx
(dv)/(dt)=-2sqrt(v)	\frac{dv}{dt}=-2\sqrt{v}
integral from 2 to 4 of 1/((x-3)^2)	\int\:_{2}^{4}\frac{1}{(x-3)^{2}}dx
integral of 27(sec^2(x)-1)tan(x)sec(x)	\int\:27(\sec^{2}(x)-1)\tan(x)\sec(x)dx
limit as x approaches 20 of x	\lim\:_{x\to\:20}(x)
integral of e^{-x}sqrt(1+e^{-2x)}	\int\:e^{-x}\sqrt{1+e^{-2x}}dx
integral of 4e^{2x}sin(2x)	\int\:4e^{2x}\sin(2x)dx
tangent of ((sqrt(x)+1))/((sqrt(x)+3))	tangent\:\frac{(\sqrt{x}+1)}{(\sqrt{x}+3)}
integral of 2xcos(x/3)	\int\:2x\cos(\frac{x}{3})dx
integral of e^{10x}(10)	\int\:e^{10x}(10)dx
integral of xcsc(tan(x^2))sec^2(x^2)	\int\:x\csc(\tan(x^{2}))\sec^{2}(x^{2})dx
(\partial)/(\partial x)(x^4+5xy^3)	\frac{\partial\:}{\partial\:x}(x^{4}+5xy^{3})
integral of (x^2)/(x^2+x+30)	\int\:\frac{x^{2}}{x^{2}+x+30}dx
tangent of f(x)=sqrt(2x+3),\at x=3	tangent\:f(x)=\sqrt{2x+3},\at\:x=3
integral from 0 to pi of 3x^2+cos(x)	\int\:_{0}^{π}3x^{2}+\cos(x)dx
derivative of x/(x^{-1)+12}	derivative\:\frac{x}{x^{-1}+12}
derivative of (-x^2+1/((x^2+1)^2))	\frac{d}{dx}(\frac{-x^{2}+1}{(x^{2}+1)^{2}})
(\partial)/(\partial x)(e^{-x}*y)	\frac{\partial\:}{\partial\:x}(e^{-x}\cdot\:y)
derivative of arcsec(2x)	derivative\:\arcsec(2x)
integral of (x+2)/(x^2-2x-15)	\int\:\frac{x+2}{x^{2}-2x-15}dx
limit as x approaches 1 of 3(x-1)^2	\lim\:_{x\to\:1}(3(x-1)^{2})
implicit tan(x/y)=x+y	implicit\:\tan(\frac{x}{y})=x+y
tangent of f(x)=arctan(x/2),\at x=2	tangent\:f(x)=\arctan(\frac{x}{2}),\at\:x=2
area 2x+6,-2,2	area\:2x+6,-2,2
tangent of y=ln(x^2-2x+1),(2,0)	tangent\:y=\ln(x^{2}-2x+1),(2,0)
derivative of 2^{sin(x})	\frac{d}{dx}(2^{\sin(x)})
integral from 0 to 4 of (ln(x))/(sqrt(x))	\int\:_{0}^{4}\frac{\ln(x)}{\sqrt{x}}dx
maclaurin sin^2(x)	maclaurin\:\sin^{2}(x)
d/(dt)(3cos(t))	\frac{d}{dt}(3\cos(t))
limit as x approaches 0 of 3ln(x)	\lim\:_{x\to\:0}(3\ln(x))
integral of sin^3(t)cos^8(t)	\int\:\sin^{3}(t)\cos^{8}(t)dt
integral from 0 to pi/3 of sin(3t)	\int\:_{0}^{\frac{π}{3}}\sin(3t)dt
integral of 5/(x^2-5)	\int\:\frac{5}{x^{2}-5}dx
derivative of (x^2+x-6/(x^2-4x+3))	\frac{d}{dx}(\frac{x^{2}+x-6}{x^{2}-4x+3})
derivative of 4sec(xtan(x))	\frac{d}{dx}(4\sec(x)\tan(x))
y^{''}+2y^'+10y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+10y=0,y(0)=1,y^{\prime\:}(0)=0
integral of x^{11}sqrt(x^6+4)	\int\:x^{11}\sqrt{x^{6}+4}dx
integral of 7v(v^2+2)^2	\int\:7v(v^{2}+2)^{2}dv
d/(dθ)(3+2sin(θ))	\frac{d}{dθ}(3+2\sin(θ))
f(x)=(sqrt(x)+x)/(x^2)	f(x)=\frac{\sqrt{x}+x}{x^{2}}
derivative of-(14)/(s^5)	derivative\:-\frac{14}{s^{5}}
derivative of f(x)=\sqrt[3]{4-9x}	derivative\:f(x)=\sqrt[3]{4-9x}

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