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Popular Calculus Problems

derivative of ln(x+\sqrt[5]{x^3})	\frac{d}{dx}(\ln(x)+\sqrt[5]{x^{3}})
limit as x approaches 0 of a^x+a^{-x}	\lim\:_{x\to\:0}(a^{x}+a^{-x})
integral of (3x+4)^6	\int\:(3x+4)^{6}dx
y^'+e^xy=19e^x	y^{\prime\:}+e^{x}y=19e^{x}
(\partial)/(\partial w)((y-w(x+x^2))^2)	\frac{\partial\:}{\partial\:w}((y-w(x+x^{2}))^{2})
limit as x approaches 1/2 of 1/(2x-1)	\lim\:_{x\to\:\frac{1}{2}}(\frac{1}{2x-1})
integral of ((x^3))/(sqrt(x^2+36))	\int\:\frac{(x^{3})}{\sqrt{x^{2}+36}}dx
x^2(dy)/(dx)= 1/4 x^2+y^2	x^{2}\frac{dy}{dx}=\frac{1}{4}x^{2}+y^{2}
limit as t approaches 0 of e^{-7t}i+(t^2)/(sin^2(t))j+tan(3tk)	\lim\:_{t\to\:0}(e^{-7t}i+\frac{t^{2}}{\sin^{2}(t)}j+\tan(3tk))
derivative of f(x)=sin(x^2+1)	derivative\:f(x)=\sin(x^{2}+1)
integral of 2x^3*e^{-x^2}	\int\:2x^{3}\cdot\:e^{-x^{2}}dx
y^{''}+4y=8cos(2x)	y^{\prime\:\prime\:}+4y=8\cos(2x)
(dy)/(dt)=ky(1-y)	\frac{dy}{dt}=ky(1-y)
integral of xsqrt(x^2+5)	\int\:x\sqrt{x^{2}+5}dx
integral of (-x+3)^2	\int\:(-x+3)^{2}dx
(ln(ln(x)))^'	(\ln(\ln(x)))^{\prime\:}
derivative of f(x)=x^3(3-x)^2	derivative\:f(x)=x^{3}(3-x)^{2}
derivative of y=cot^2(sin(x))	derivative\:y=\cot^{2}(\sin(x))
(\partial)/(\partial x)((e/y)^x)	\frac{\partial\:}{\partial\:x}((\frac{e}{y})^{x})
integral from 0 to 4 of (3t^4+3t+2)	\int\:_{0}^{4}(3t^{4}+3t+2)dt
(\partial)/(\partial y)(2x+4y)	\frac{\partial\:}{\partial\:y}(2x+4y)
derivative of f(x)=2sqrt(x)-1	derivative\:f(x)=2\sqrt{x}-1
limit as x approaches infinity of e^{-x}-ln(x)	\lim\:_{x\to\:\infty\:}(e^{-x}-\ln(x))
integral of (8x^2+x+73)/((x+1)(x^2+9))	\int\:\frac{8x^{2}+x+73}{(x+1)(x^{2}+9)}dx
derivative of 7(x^3-x)^4	derivative\:7(x^{3}-x)^{4}
derivative of (3x-8/(x^2-1))	\frac{d}{dx}(\frac{3x-8}{x^{2}-1})
y^'+(3y)/x = 3/x	y^{\prime\:}+\frac{3y}{x}=\frac{3}{x}
derivative of y= 9/(x^{-6)}	derivative\:y=\frac{9}{x^{-6}}
inverse oflaplace {s/((s-2)(s-3)(s-6))}	inverselaplace\:\left\{\frac{s}{(s-2)(s-3)(s-6)}\right\}
derivative of (x+ae^{3x}+b)	\frac{d}{dx}((x+a)e^{3x}+b)
derivative of 4x^{-3}+6x^{-8/3}	derivative\:4x^{-3}+6x^{-\frac{8}{3}}
(\partial)/(\partial x)(arcsin(3x+y))	\frac{\partial\:}{\partial\:x}(\arcsin(3x+y))
derivative of f(x)=6e^xcos(x)	derivative\:f(x)=6e^{x}\cos(x)
area y^2=x+2,y^2=2-x	area\:y^{2}=x+2,y^{2}=2-x
derivative of f(x)=-7/((x-7)^2)	derivative\:f(x)=-\frac{7}{(x-7)^{2}}
integral of sin^2((2pix)/L)	\int\:\sin^{2}(\frac{2πx}{L})dx
derivative of e^{(-1/(x^2)})	\frac{d}{dx}(e^{\frac{-1}{x^{2}}})
limit as x approaches 3 of (7x^2-3x)/x	\lim\:_{x\to\:3}(\frac{7x^{2}-3x}{x})
1/4 ((dy)/(dt))+10y=5	\frac{1}{4}(\frac{dy}{dt})+10y=5
integral of sec^2(xta)n^2x	\int\:\sec^{2}(xta)n^{2}xdx
tangent of f(x)=x^3-3/2 x^2+x,\at x=1	tangent\:f(x)=x^{3}-\frac{3}{2}x^{2}+x,\at\:x=1
sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n))	\sum\:_{n=2}^{\infty\:}\frac{(-1)^{n}}{\sqrt{n}\ln(n)}
integral of sqrt(4+y^2)	\int\:\sqrt{4+y^{2}}dy
integral of (14)/((x-1)^2(x-2)^2)	\int\:\frac{14}{(x-1)^{2}(x-2)^{2}}dx
f(x)=arcsin(4x)	f(x)=\arcsin(4x)
limit as x approaches infinity of arctan(x^2-x^5)	\lim\:_{x\to\:\infty\:}(\arctan(x^{2}-x^{5}))
tangent of y=e^xln(x),(1,0)	tangent\:y=e^{x}\ln(x),(1,0)
(\partial)/(\partial y)(e^xy^2)	\frac{\partial\:}{\partial\:y}(e^{x}y^{2})
derivative of tan(x-1)	\frac{d}{dx}(\tan(x)-1)
slope of (2.4)(0.8)	slope\:(2.4)(0.8)
(dr)/(dt)=(sec^2(t))/(tan(t)+1)	\frac{dr}{dt}=\frac{\sec^{2}(t)}{\tan(t)+1}
integral of (9/x+6/(x^4))	\int\:(\frac{9}{x}+\frac{6}{x^{4}})dx
(1/(x-2))^'	(\frac{1}{x-2})^{\prime\:}
derivative of y^3+xy^2+y+xcos(3x-2)	\frac{d}{dx}(y^{3}+xy^{2}+y+x\cos(3x)-2)
derivative of ((x^2-4)/(x-2))	\frac{d}{dx}(\frac{(x^{2}-4)}{x-2})
derivative of (1+sqrt(X))/(1-sqrt(X))	derivative\:\frac{1+\sqrt{X}}{1-\sqrt{X}}
integral of e^{cos(25t)}sin(25t)	\int\:e^{\cos(25t)}\sin(25t)dt
tangent of x+5/x	tangent\:x+\frac{5}{x}
(xdy)/(dx)-y=x^{2017}*y^2	\frac{xdy}{dx}-y=x^{2017}\cdot\:y^{2}
(\partial)/(\partial x)((2-xy)e^{-xy})	\frac{\partial\:}{\partial\:x}((2-xy)e^{-xy})
(\partial)/(\partial x)((2x+2y)e^y)	\frac{\partial\:}{\partial\:x}((2x+2y)e^{y})
integral of (2y)/(x^2+1)	\int\:\frac{2y}{x^{2}+1}dy
integral of x+y+z	\int\:x+y+zdx
derivative of-2x^2+3x-4	\frac{d}{dx}(-2x^{2}+3x-4)
(dy}{dx}=\frac{3y)/x ,x>0	\frac{dy}{dx}=\frac{3y}{x},x>0
integral of 3/(xln(x))	\int\:\frac{3}{x\ln(x)}dx
derivative of (x^3/(39)+(13)/(4x))	\frac{d}{dx}(\frac{x^{3}}{39}+\frac{13}{4x})
derivative of f(x)= 2/(t^3)	derivative\:f(x)=\frac{2}{t^{3}}
implicit (d^2y)/(dx^2),x^2+y^2=16	implicit\:\frac{d^{2}y}{dx^{2}},x^{2}+y^{2}=16
(\partial)/(\partial z)(xy+yz-xz)	\frac{\partial\:}{\partial\:z}(xy+yz-xz)
sqrt(1-y^2)dx=sqrt(1-x^2)dy	\sqrt{1-y^{2}}dx=\sqrt{1-x^{2}}dy
integral from 0 to 2 of (2x)/((x^2+5)^3)	\int\:_{0}^{2}\frac{2x}{(x^{2}+5)^{3}}dx
limit as x approaches 0 of (-2e^{-x})/(2x-2)	\lim\:_{x\to\:0}(\frac{-2e^{-x}}{2x-2})
integral of (e^{4x})/(-4x)	\int\:\frac{e^{4x}}{-4x}dx
(1+x^2)(1+y^2)dx-xydy=0	(1+x^{2})(1+y^{2})dx-xydy=0
limit as x approaches+0 of ((3e^x-3))/x	\lim\:_{x\to\:+0}(\frac{(3e^{x}-3)}{x})
integral from 0 to 1 of 0.5e^{-2x}	\int\:_{0}^{1}0.5e^{-2x}dx
integral of 2xx	\int\:2xxdx
derivative of (x+1)/(3x^2+6x+7)	derivative\:\frac{x+1}{3x^{2}+6x+7}
integral of sin^2(wt)	\int\:\sin^{2}(wt)dt
maclaurin arctan(4x)	maclaurin\:\arctan(4x)
derivative of (x^{-2}+x^3*(4x)^{-2x})	\frac{d}{dx}((x^{-2}+x)^{3}\cdot\:(4x)^{-2x})
(\partial)/(\partial x)(l-c)	\frac{\partial\:}{\partial\:x}(l-c)
integral of x(15x+4)	\int\:x(15x+4)dx
derivative of ((6x^2+6x+4))/(sqrt(x))	derivative\:\frac{(6x^{2}+6x+4)}{\sqrt{x}}
derivative of xy^4	\frac{d}{dx}(xy^{4})
derivative of (x^2-9^3)	\frac{d}{dx}((x^{2}-9)^{3})
integral of x^{37}sin(x^{38})	\int\:x^{37}\sin(x^{38})dx
integral of sec(x/8)	\int\:\sec(\frac{x}{8})dx
integral from 8 to infinity of xe^{-5x}	\int\:_{8}^{\infty\:}xe^{-5x}dx
integral of ((ln(x))^{12})/x	\int\:\frac{(\ln(x))^{12}}{x}dx
derivative of 12e^{x/2}	\frac{d}{dx}(12e^{\frac{x}{2}})
integral of (e^x(xln(x)+1))/x	\int\:\frac{e^{x}(x\ln(x)+1)}{x}dx
derivative of (3x+8)/(x^2)	derivative\:\frac{3x+8}{x^{2}}
inverse oflaplace ((3s+1))/(s+2)	inverselaplace\:\frac{(3s+1)}{s+2}
(\partial)/(\partial y)(x/((x+y)^2))	\frac{\partial\:}{\partial\:y}(\frac{x}{(x+y)^{2}})
integral from 1 to 3 of (x^3+1/(4x^3))	\int\:_{1}^{3}(x^{3}+\frac{1}{4x^{3}})dx
normal of y=2x-1+4x^2,(1,5)	normal\:y=2x-1+4x^{2},(1,5)
integral of ke^{-x}	\int\:ke^{-x}dx
(\partial)/(\partial x)(y(e^x+xe^x))	\frac{\partial\:}{\partial\:x}(y(e^{x}+xe^{x}))

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