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Popular Calculus Problems

limit as x approaches+0 of (1-1/x)x	\lim\:_{x\to\:+0}((1-\frac{1}{x})x)
(\partial)/(\partial y)(x+y+1)	\frac{\partial\:}{\partial\:y}(x+y+1)
integral of 1/(x^{2022)}	\int\:\frac{1}{x^{2022}}dx
d/(dt)(7t^3)	\frac{d}{dt}(7t^{3})
inverse oflaplace 1/(s(4s^2-1))	inverselaplace\:\frac{1}{s(4s^{2}-1)}
integral of 1/(x^2-6x)	\int\:\frac{1}{x^{2}-6x}dx
integral of 1/(4x+xln^2(3x))	\int\:\frac{1}{4x+x\ln^{2}(3x)}dx
integral of sec(t)(2sec(t)+7tan(t))	\int\:\sec(t)(2\sec(t)+7\tan(t))dt
(dy)/(dx)=x+4y-2	\frac{dy}{dx}=x+4y-2
integral of (6x^3+4x^2-2x)/(2x^2)	\int\:\frac{6x^{3}+4x^{2}-2x}{2x^{2}}dx
(\partial)/(\partial x)(x^3-xsin(y))	\frac{\partial\:}{\partial\:x}(x^{3}-x\sin(y))
integral from-1 to 0 of x^3-x	\int\:_{-1}^{0}x^{3}-xdx
integral of x(sqrt(16-x^2))	\int\:x(\sqrt{16-x^{2}})dx
limit as x approaches 2 of (5x)/(x-2)	\lim\:_{x\to\:2}(\frac{5x}{x-2})
integral of e^{2θ}sin(3θ)	\int\:e^{2θ}\sin(3θ)dθ
(ln(f(x)))'	(\ln(f(x)))\prime\:
inverse oflaplace 10s	inverselaplace\:10s
(3^{-x^2})^'	(3^{-x^{2}})^{\prime\:}
derivative of 1-(36)/(x^2)	derivative\:1-\frac{36}{x^{2}}
(dx)/(dt)=ax+b	\frac{dx}{dt}=ax+b
derivative of 7cos(4x)	derivative\:7\cos(4x)
-2y^{''}+4y^'+3y=1	-2y^{\prime\:\prime\:}+4y^{\prime\:}+3y=1
f(x)=(x^2+2)(x^4+1)	f(x)=(x^{2}+2)(x^{4}+1)
cos(t)y^'-sin(t)y=t^2	\cos(t)y^{\prime\:}-\sin(t)y=t^{2}
simplify x/(x+c/x)	simplify\:\frac{x}{x+\frac{c}{x}}
derivative of sqrt(7)x+sqrt(6x)	derivative\:\sqrt{7}x+\sqrt{6x}
tangent of f(x)=5x^{3/5}-4	tangent\:f(x)=5x^{\frac{3}{5}}-4
integral of (Inx)/((x+1)^2)	\int\:\frac{Inx}{(x+1)^{2}}dx
limit as x approaches infinity of 4-x^2	\lim\:_{x\to\:\infty\:}(4-x^{2})
derivative of 2sec(3x^2)	\frac{d}{dx}(2\sec(3x^{2}))
tangent of y=(x^3-9x)^{12}	tangent\:y=(x^{3}-9x)^{12}
limit as x approaches x/8 of tan(24*x)	\lim\:_{x\to\:\frac{x}{8}}(\tan(24\cdot\:x))
integral of csc^4(4x)	\int\:\csc^{4}(4x)dx
derivative of (4-sqrt(x)^2)	\frac{d}{dx}((4-\sqrt{x})^{2})
integral of (100)/(25+(5y)^2)+e^4	\int\:\frac{100}{25+(5y)^{2}}+e^{4}dy
derivative of (y(4x+4y))/((x^2+y^2))	derivative\:\frac{y(4x+4y)}{(x^{2}+y^{2})}
integral from 1 to 4 of x^2+2	\int\:_{1}^{4}x^{2}+2dx
(\partial)/(\partial x)(2x^{3y})	\frac{\partial\:}{\partial\:x}(2x^{3y})
(\partial)/(\partial t)(-3st)	\frac{\partial\:}{\partial\:t}(-3st)
tangent of (0.1666)(0.998)^x	tangent\:(0.1666)(0.998)^{x}
derivative of (2x^2-5x+4/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}-5x+4}{\sqrt{x}})
area y=sqrt(x+4),y= x/2+2	area\:y=\sqrt{x+4},y=\frac{x}{2}+2
integral of 8tan^4(xse)c^6x	\int\:8\tan^{4}(xse)c^{6}xdx
derivative of e^{1/2 x}	derivative\:e^{\frac{1}{2}x}
area 4-4cos(7x),4cos(7x),0>= x>= pi/7	area\:4-4\cos(7x),4\cos(7x),0\ge\:x\ge\:\frac{π}{7}
derivative of 2xsqrt(x)+1/(sqrt(x))	\frac{d}{dx}(2x\sqrt{x}+\frac{1}{\sqrt{x}})
integral of x^2+7	\int\:x^{2}+7dx
y^{''}=-3y-2y^',y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}=-3y-2y^{\prime\:},y(0)=1,y^{\prime\:}(0)=0
integral of 4/(1+x^2)	\int\:\frac{4}{1+x^{2}}dx
3y^'-2y=e^{-pi/2}	3y^{\prime\:}-2y=e^{-\frac{π}{2}}
derivative of y=x^{2cos(x)}	derivative\:y=x^{2\cos(x)}
derivative of 3-\|x-3\|	\frac{d}{dx}(3-\left\|x-3\right\|)
sum from n=0 to infinity of 7(-1/8)^n	\sum\:_{n=0}^{\infty\:}7(-\frac{1}{8})^{n}
xy^'+4y=2x^3	xy^{\prime\:}+4y=2x^{3}
tangent of y=sqrt(7x+2),(2,4)	tangent\:y=\sqrt{7x+2},(2,4)
integral of e^{-16x}	\int\:e^{-16x}dx
derivative of 1-e^{-x}sin(y)	\frac{d}{dx}(1-e^{-x}\sin(y))
derivative of sqrt(x/(x^2+5))	\frac{d}{dx}(\sqrt{\frac{x}{x^{2}+5}})
(\partial)/(\partial x)(1/(sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x}})
area x^2=y^3,x=3y	area\:x^{2}=y^{3},x=3y
inverse oflaplace 1/((s-1)(s^2+9))	inverselaplace\:\frac{1}{(s-1)(s^{2}+9)}
integral of arctan(5x)	\int\:\arctan(5x)dx
integral of-e^{4x}+4x^5	\int\:-e^{4x}+4x^{5}dx
tangent of f(x)=sqrt(x),\at x=36	tangent\:f(x)=\sqrt{x},\at\:x=36
derivative of f(x)=4x^3+9	derivative\:f(x)=4x^{3}+9
(-x^{-2})^'	(-x^{-2})^{\prime\:}
(x^2+2x-1)y^'-(x+1)y=x-1	(x^{2}+2x-1)y^{\prime\:}-(x+1)y=x-1
limit as x approaches 0 of x^4cos(5/x)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{5}{x}))
integral of t^2(t^3-4)^2	\int\:t^{2}(t^{3}-4)^{2}dt
slope of (x-2)^4+e^{x-2}+(x-2*z)^2	slope\:(x-2)^{4}+e^{x-2}+(x-2\cdot\:z)^{2}
(dy)/(dx)=x+7y	\frac{dy}{dx}=x+7y
integral of 27x^{26}	\int\:27x^{26}dx
inverse oflaplace (-5s)/((s^2+1)^2)	inverselaplace\:\frac{-5s}{(s^{2}+1)^{2}}
limit as x approaches 1 of 3/(x-1)	\lim\:_{x\to\:1}(\frac{3}{x-1})
(\partial)/(\partial x)(sqrt(8-x^2))	\frac{\partial\:}{\partial\:x}(\sqrt{8-x^{2}})
integral from 1 to 100 of (21)/(x^3)	\int\:_{1}^{100}\frac{21}{x^{3}}dx
derivative of ln(x+sqrt(x^2-7))	derivative\:\ln(x+\sqrt{x^{2}-7})
2y^{''}-6y^'+5y=0	2y^{\prime\:\prime\:}-6y^{\prime\:}+5y=0
integral of cot(15x)	\int\:\cot(15x)dx
(\partial)/(\partial s)(sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:s}(\sqrt{s^{2}+t^{2}})
sum from n=0 to infinity of nsin(n*pi)	\sum\:_{n=0}^{\infty\:}n\sin(n\cdot\:π)
inverse oflaplace (s+1)/((s(s^2+s+1)))	inverselaplace\:\frac{s+1}{(s(s^{2}+s+1))}
(\partial)/(\partial x)(e^{cos(x)})	\frac{\partial\:}{\partial\:x}(e^{\cos(x)})
derivative of (8x+9(9x-10))	\frac{d}{dx}((8x+9)(9x-10))
integral of (csc^4(x))/(cot^2(x))	\int\:\frac{\csc^{4}(x)}{\cot^{2}(x)}dx
integral of x^2-4x+4	\int\:x^{2}-4x+4dx
(dy)/(dx)=(cos(12x))/(e^{12y)}	\frac{dy}{dx}=\frac{\cos(12x)}{e^{12y}}
integral from 1 to 2 of (15)/(x^3+5x)	\int\:_{1}^{2}\frac{15}{x^{3}+5x}dx
simplify xL(x)-x	simplify\:xL(x)-x
y^{''}-y^'-6y=0,y(0)=0,y^'(0)=4	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=0,y^{\prime\:}(0)=4
integral of (18)/((x+3)(x^2+9))	\int\:\frac{18}{(x+3)(x^{2}+9)}dx
limit as x approaches 2 of-6	\lim\:_{x\to\:2}(-6)
derivative of pix	\frac{d}{dx}(πx)
integral of 1/(9x^2-18x+72)	\int\:\frac{1}{9x^{2}-18x+72}dx
integral of-4ln(2x+1)	\int\:-4\ln(2x+1)dx
simplify (y^{-1}+y^{-2})(2y^{-3}-6y^{-4})	simplify\:(y^{-1}+y^{-2})(2y^{-3}-6y^{-4})
limit as x approaches infinity of 1/(x*log_{e)(x)}	\lim\:_{x\to\:\infty\:}(\frac{1}{x\cdot\:\log_{e}(x)})
limit as x approaches 2-of (x-2)/(x-2)	\lim\:_{x\to\:2-}(\frac{x-2}{x-2})
limit as x approaches infinity of 1+a/x	\lim\:_{x\to\:\infty\:}(1+\frac{a}{x})
integral of 3/((5v-1)^4)	\int\:\frac{3}{(5v-1)^{4}}dv

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