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Popular Calculus Problems

limit as x approaches 3+of (x^2-9)^{x-3}	\lim\:_{x\to\:3+}((x^{2}-9)^{x-3})
integral of (t^2+8)/(t^2-5t+6)	\int\:\frac{t^{2}+8}{t^{2}-5t+6}dt
tangent of 3x^2+4x	tangent\:3x^{2}+4x
integral of \|x-5\|	\int\:\left\|x-5\right\|dx
limit as x approaches 0 of 1/(ln\|x\|)	\lim\:_{x\to\:0}(\frac{1}{\ln\left\|x\right\|})
integral of (15xe^{2x})/((1+2x)^2)	\int\:\frac{15xe^{2x}}{(1+2x)^{2}}dx
implicit (dy)/(dx),e^{5y^2}=x^3+3	implicit\:\frac{dy}{dx},e^{5y^{2}}=x^{3}+3
y^'=(x-2)e^{-2y},y(2)=ln(2)	y^{\prime\:}=(x-2)e^{-2y},y(2)=\ln(2)
(\partial)/(\partial y)(xe^{x/y})	\frac{\partial\:}{\partial\:y}(xe^{\frac{x}{y}})
integral from 25 to 50 of 20	\int\:_{25}^{50}20dx
derivative of f(x)=(x^2+1)/(x+4)	derivative\:f(x)=\frac{x^{2}+1}{x+4}
derivative of f(x)=x^{5/2}(2-5x^3)	derivative\:f(x)=x^{\frac{5}{2}}(2-5x^{3})
laplacetransform e^{(-2x)}(3x)^2	laplacetransform\:e^{(-2x)}(3x)^{2}
tangent of f(x)=-5sin(x),\at x= pi/4	tangent\:f(x)=-5\sin(x),\at\:x=\frac{π}{4}
integral of (4x^2+3x-7)	\int\:(4x^{2}+3x-7)dx
derivative of x^2y^3+x^3y^2	\frac{d}{dx}(x^{2}y^{3}+x^{3}y^{2})
integral of (3-3x)/(1-sqrt(x))	\int\:\frac{3-3x}{1-\sqrt{x}}dx
(\partial)/(\partial x)(6xy+2*y)	\frac{\partial\:}{\partial\:x}(6\cdot\:x\cdot\:y+2\cdot\:y)
derivative of (x-1^4)	\frac{d}{dx}((x-1)^{4})
derivative of x/(x^2)	\frac{d}{dx}(\frac{x}{x^{2}})
integral of sqrt(144-x^2)	\int\:\sqrt{144-x^{2}}dx
limit as x approaches-1 of x^3+2x^2-3x-4	\lim\:_{x\to\:-1}(x^{3}+2x^{2}-3x-4)
(dy)/(dx)=(xy)^2	\frac{dy}{dx}=(xy)^{2}
derivative of x^{(2)}sin(x)	derivative\:x^{(2)}\sin(x)
integral from 0 to pi/2 of sin^3(3x)	\int\:_{0}^{\frac{π}{2}}\sin^{3}(3x)dx
tangent of (2x-1)^2ln(2x-1)	tangent\:(2x-1)^{2}\ln(2x-1)
(dy)/(dx)=y(1-y),y(0)=2	\frac{dy}{dx}=y(1-y),y(0)=2
derivative of (-2x^2+2/((1+x^2)^2))	\frac{d}{dx}(\frac{-2x^{2}+2}{(1+x^{2})^{2}})
(\partial)/(\partial x)(-4y(-2x-y-3))	\frac{\partial\:}{\partial\:x}(-4y(-2x-y-3))
integral of 1-(16)/(sin^4(x))	\int\:1-\frac{16}{\sin^{4}(x)}dx
limit as x approaches 0 of xln^2(x)	\lim\:_{x\to\:0}(x\ln^{2}(x))
(\partial)/(\partial x)(3y^2-x^2)	\frac{\partial\:}{\partial\:x}(3y^{2}-x^{2})
derivative of (x^2+4/(4x^3-5x))	\frac{d}{dx}(\frac{x^{2}+4}{4x^{3}-5x})
derivative of-5e^{-5x+2}	derivative\:-5e^{-5x+2}
integral of (e^x)/(e^x+e)	\int\:\frac{e^{x}}{e^{x}+e}dx
integral of 1/(sqrt(y))	\int\:\frac{1}{\sqrt{y}}dy
derivative of 1/(2sqrt(x+1))	derivative\:\frac{1}{2\sqrt{x+1}}
integral from-pi to 2pi of picos^2(x)	\int\:_{-π}^{2π}π\cos^{2}(x)dx
derivative of f(x)=3x^2e^x+e^x(x^3+2)	derivative\:f(x)=3x^{2}e^{x}+e^{x}(x^{3}+2)
integral of (sqrt(49+x^2))/x	\int\:\frac{\sqrt{49+x^{2}}}{x}dx
limit as x approaches 2+of (5+x)/(2-x)	\lim\:_{x\to\:2+}(\frac{5+x}{2-x})
inverse oflaplace 1/(s^6)	inverselaplace\:\frac{1}{s^{6}}
derivative of e^{-st}	derivative\:e^{-st}
integral of sin(3x)cos(6x)	\int\:\sin(3x)\cos(6x)dx
integral from 1 to 2 of e^x	\int\:_{1}^{2}e^{x}dx
integral of xe^{-ax}	\int\:xe^{-ax}dx
inverse oflaplace 1/((1+s^2)(s^2+3))	inverselaplace\:\frac{1}{(1+s^{2})(s^{2}+3)}
integral from 0 to 1 of \|x\|	\int\:_{0}^{1}\left\|x\right\|dx
tangent of f(x)=x+sqrt(x),\at x=1	tangent\:f(x)=x+\sqrt{x},\at\:x=1
integral from 0 to 1 of 2^{-θ}	\int\:_{0}^{1}2^{-θ}dθ
limit as x approaches 0 of 3x-4	\lim\:_{x\to\:0}(3x-4)
d/(dy)(cos(xy))	\frac{d}{dy}(\cos(xy))
(dy)/(dt)= t/(t^2y+y)	\frac{dy}{dt}=\frac{t}{t^{2}y+y}
(d^2)/(dx^2)((x^2+6)^4)	\frac{d^{2}}{dx^{2}}((x^{2}+6)^{4})
integral of x^{(-1)/2}	\int\:x^{\frac{-1}{2}}dx
integral of (cos^2(x))/(sin^4(x))	\int\:\frac{\cos^{2}(x)}{\sin^{4}(x)}dx
sum from n=3 to infinity of 5/(9^n)	\sum\:_{n=3}^{\infty\:}\frac{5}{9^{n}}
(\partial)/(\partial y)(x-y^3+y^2sin(x))	\frac{\partial\:}{\partial\:y}(x-y^{3}+y^{2}\sin(x))
derivative of e^{(2/x)}	derivative\:e^{(\frac{2}{x})}
integral from-2 to 2 of-3\|x^2-4x\|	\int\:_{-2}^{2}-3\left\|x^{2}-4x\right\|dx
integral of 5/(x^2+3x-4)	\int\:\frac{5}{x^{2}+3x-4}dx
integral of (5x-3)^4	\int\:(5x-3)^{4}dx
slope of y=(x^2)/3+x+1/2	slope\:y=\frac{x^{2}}{3}+x+\frac{1}{2}
derivative of (90)/x	derivative\:\frac{90}{x}
integral from 0 to 2 of x/((1+x^2)^2)	\int\:_{0}^{2}\frac{x}{(1+x^{2})^{2}}dx
derivative of (5-6x^5)	\frac{d}{dx}((5-6x)^{5})
simplify 2x+3/x	simplify\:2x+\frac{3}{x}
limit as x approaches infinity of xe^{-1}	\lim\:_{x\to\:\infty\:}(xe^{-1})
(\partial)/(\partial x)(x/(sqrt(1+x^2)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sqrt{1+x^{2}}})
(x^2+1)(dy)/(dx)+xy=4sqrt(1+x^2)	(x^{2}+1)\frac{dy}{dx}+xy=4\sqrt{1+x^{2}}
tangent of 4x^2-x^3	tangent\:4x^{2}-x^{3}
integral from-infinity to 0 of 1/(5-10x)	\int\:_{-\infty\:}^{0}\frac{1}{5-10x}dx
integral of pi/2	\int\:\frac{π}{2}
derivative of (ln(x)^4)	\frac{d}{dx}((\ln(x))^{4})
f(x)=3tan(x)	f(x)=3\tan(x)
tangent of y=x^2-5x+5,(4,1)	tangent\:y=x^{2}-5x+5,(4,1)
derivative of (3x^2e^x-4/(x^2))	\frac{d}{dx}(\frac{3x^{2}e^{x}-4}{x^{2}})
5y^'=y^2,y(0)=1	5y^{\prime\:}=y^{2},y(0)=1
integral from 0 to 1 of (x^2)/(x^2+1)	\int\:_{0}^{1}\frac{x^{2}}{x^{2}+1}dx
derivative of 1-2/x	\frac{d}{dx}(1-\frac{2}{x})
y^{''}+xy^'-y=0	y^{\prime\:\prime\:}+xy^{\prime\:}-y=0
derivative of-(cos(x)/(sqrt(x)))	\frac{d}{dx}(-\frac{\cos(x)}{\sqrt{x}})
integral of (5x^3)/(x^2-1)	\int\:\frac{5x^{3}}{x^{2}-1}dx
y^{''}+3y^'+2y=(1+e^t)^{-1}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=(1+e^{t})^{-1}
derivative of 4x^{-3}	derivative\:4x^{-3}
limit as x approaches-5 of \|x\|-5	\lim\:_{x\to\:-5}(\left\|x\right\|-5)
taylor (1-x)^{-100}	taylor\:(1-x)^{-100}
laplacetransform e^{-0.4t}cos(12t)	laplacetransform\:e^{-0.4t}\cos(12t)
integral of (2x)/(sqrt(x^2+4))	\int\:\frac{2x}{\sqrt{x^{2}+4}}dx
limit as T approaches infinity of f(T)	\lim\:_{T\to\:\infty\:}(f(T))
integral of sec^5(3x)tan(3x)	\int\:\sec^{5}(3x)\tan(3x)dx
derivative of x/y	derivative\:\frac{x}{y}
integral of 1/((x^2-144)^{3/2)}	\int\:\frac{1}{(x^{2}-144)^{\frac{3}{2}}}dx
(dy)/(dx)=6y^{2/3}	\frac{dy}{dx}=6y^{\frac{2}{3}}
integral of (ln(x))/(81)	\int\:\frac{\ln(x)}{81}dx
integral of x^3e^{-2x^2}	\int\:x^{3}e^{-2x^{2}}dx
xy^'+y=2e^{2x}	xy^{\prime\:}+y=2e^{2x}
f(x)=x^9	f(x)=x^{9}
integral of 8tan^2(x)+tan^4(x)	\int\:8\tan^{2}(x)+\tan^{4}(x)dx
area y^2=4x+4,y=4x+16	area\:y^{2}=4x+4,y=4x+16

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