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Popular Calculus Problems

integral of 1/(sqrt(1-e^x))	\int\:\frac{1}{\sqrt{1-e^{x}}}dx
(\partial)/(\partial x)(x^4y^3-y^4)	\frac{\partial\:}{\partial\:x}(x^{4}y^{3}-y^{4})
d/(d{y)}(ln({x}+2{y}+3{z}))	\frac{d}{d{y}}(\ln({x}+2{y}+3{z}))
limit as x approaches 5-of 2/(x-5)+1	\lim\:_{x\to\:5-}(\frac{2}{x-5}+1)
derivative of-4x^2+1	derivative\:-4x^{2}+1
(\partial)/(\partial y)(sin(x^5-7y))	\frac{\partial\:}{\partial\:y}(\sin(x^{5}-7y))
(dy)/(dx)=(4/(x^2+1))(y+1)	\frac{dy}{dx}=(\frac{4}{x^{2}+1})(y+1)
y^{''}+4y=e^x	y^{\prime\:\prime\:}+4y=e^{x}
maclaurin φ^3cos(φ^5)	maclaurin\:φ^{3}\cos(φ^{5})
integral of 1/(x^2sqrt(x^2-1))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-1}}dx
derivative of f(x)=cos(8x^2-16)sin(x^2)	derivative\:f(x)=\cos(8x^{2}-16)\sin(x^{2})
derivative of (3/5 x)^5	derivative\:(\frac{3}{5}x)^{5}
tangent of 1/(sqrt(9x))	tangent\:\frac{1}{\sqrt{9x}}
integral of (37x+5)/((6x+1)(x-1))	\int\:\frac{37x+5}{(6x+1)(x-1)}dx
derivative of f(x)=x*ln(x)	derivative\:f(x)=x\cdot\:\ln(x)
(\partial)/(\partial x)(x^8+6xy^7)	\frac{\partial\:}{\partial\:x}(x^{8}+6xy^{7})
derivative of 6+1/(x^2)	derivative\:6+\frac{1}{x^{2}}
y^{''}+4y=3cos(2t)-5sin(2t)	y^{\prime\:\prime\:}+4y=3\cos(2t)-5\sin(2t)
tangent of y=x^4-4x^2+10,\at x=1	tangent\:y=x^{4}-4x^{2}+10,\at\:x=1
derivative of e^{-x}cos(2x)	\frac{d}{dx}(e^{-x}\cos(2x))
integral from 0 to 1 of x/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{x}{\sqrt{1-x^{2}}}dx
(xdy)/(dx)=5xe^x-y+6x^2	\frac{xdy}{dx}=5xe^{x}-y+6x^{2}
integral of (x^5-4x)^2(5x^4-4)	\int\:(x^{5}-4x)^{2}(5x^{4}-4)dx
limit as x approaches 0+of 1/(1+1/x)	\lim\:_{x\to\:0+}(\frac{1}{1+\frac{1}{x}})
derivative of-8	\frac{d}{dx}(-8)
limit as x approaches 0 of (sin^2(3x))/(5x^2)	\lim\:_{x\to\:0}(\frac{\sin^{2}(3x)}{5x^{2}})
integral of sin(4x)sin(x)	\int\:\sin(4x)\sin(x)dx
laplacetransform 2(t+2)	laplacetransform\:2(t+2)
derivative of (2x/(x^6+3x^2))	\frac{d}{dx}(\frac{2x}{x^{6}+3x^{2}})
derivative of arccos(3x)	derivative\:\arccos(3x)
integral of usin(u)	\int\:u\sin(u)du
xy+y^'=2x,y(0)=5	xy+y^{\prime\:}=2x,y(0)=5
(d^2y)/(dx^2)-3(dy)/(dx)+2y=4x^2	\frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=4x^{2}
integral of (2x^2)/(x^2+8)	\int\:\frac{2x^{2}}{x^{2}+8}dx
integral of 3x^3-2x^2+8x-6	\int\:3x^{3}-2x^{2}+8x-6dx
integral of sqrt(2)asqrt(1+cos(θ))	\int\:\sqrt{2}a\sqrt{1+\cos(θ)}dθ
derivative of cos(x-1/3 cos^3(x))	\frac{d}{dx}(\cos(x)-\frac{1}{3}\cos^{3}(x))
integral of (x-5)/(-2x+2)	\int\:\frac{x-5}{-2x+2}dx
integral of xn(1/x)	\int\:xn(\frac{1}{x})dx
integral from 0 to 1 of e^{x^2}	\int\:_{0}^{1}e^{x^{2}}dx
derivative of e^{-sx}	\frac{d}{dx}(e^{-sx})
derivative of x^2ln(x^3+1)	\frac{d}{dx}(x^{2}\ln(x^{3}+1))
integral of (2x^2-x)^2	\int\:(2x^{2}-x)^{2}dx
integral of 1/(1+\sqrt[3]{x-2)}	\int\:\frac{1}{1+\sqrt[3]{x-2}}dx
derivative of (x^5+2^2(x^4+4)^4)	\frac{d}{dx}((x^{5}+2)^{2}(x^{4}+4)^{4})
tangent of f(x)=x^4-32x^2+256,\at x=-1	tangent\:f(x)=x^{4}-32x^{2}+256,\at\:x=-1
integral of arctan(7x)	\int\:\arctan(7x)dx
laplacetransform 3e^t	laplacetransform\:3e^{t}
y^{''}+2y^'+y=e^{-t},y(0)=-1,y^'(0)=1	y^{\prime\:\prime\:}+2y^{\prime\:}+y=e^{-t},y(0)=-1,y^{\prime\:}(0)=1
derivative of (60/(x^4))	\frac{d}{dx}(\frac{60}{x^{4}})
limit as x approaches 2 of (x^2-1)/(x-1)	\lim\:_{x\to\:2}(\frac{x^{2}-1}{x-1})
sum from n=0 to infinity of arctan(n)	\sum\:_{n=0}^{\infty\:}\arctan(n)
integral from-3 to 3 of 9-x^2	\int\:_{-3}^{3}9-x^{2}dx
y^3=(dy)/(dx)+y	y^{3}=\frac{dy}{dx}+y
integral from-8 to 8 of (sqrt(64-x^2))	\int\:_{-8}^{8}(\sqrt{64-x^{2}})dx
derivative of (-2x^2+1/(sqrt(1-x^2)))	\frac{d}{dx}(\frac{-2x^{2}+1}{\sqrt{1-x^{2}}})
integral of 1/(1+2cos(x))	\int\:\frac{1}{1+2\cos(x)}dx
derivative of (x-2/(x^2))	\frac{d}{dx}(\frac{x-2}{x^{2}})
area y=4sqrt(2x),y=2x^2,y=-4x+6	area\:y=4\sqrt{2x},y=2x^{2},y=-4x+6
integral of-10cos(-2x+7)	\int\:-10\cos(-2x+7)dx
derivative of f(x)=sin(sin(x))	derivative\:f(x)=\sin(\sin(x))
x^2dx=y^3dy	x^{2}dx=y^{3}dy
derivative of log_{e}(3x^2+7)	\frac{d}{dx}(\log_{e}(3x^{2}+7))
integral of sin^3(x)cos^{-2}(x)	\int\:\sin^{3}(x)\cos^{-2}(x)dx
derivative of (1-4x/(3+x))	\frac{d}{dx}(\frac{1-4x}{3+x})
y(2x^2+5x-3)dy=e^ydx	y(2x^{2}+5x-3)dy=e^{y}dx
(\partial)/(\partial x)(xe^{7xy})	\frac{\partial\:}{\partial\:x}(xe^{7xy})
integral of (x^2+1)sqrt(2x+1)	\int\:(x^{2}+1)\sqrt{2x+1}dx
inverse oflaplace ((3se^{(-2s)}))/(4s^2+36)	inverselaplace\:\frac{(3se^{(-2s)})}{4s^{2}+36}
integral of x^2cos(x)-2xcos(x)	\int\:x^{2}\cos(x)-2x\cos(x)dx
limit as x approaches 9 of (x-9)/(\|x-9\|)	\lim\:_{x\to\:9}(\frac{x-9}{\left\|x-9\right\|})
derivative of x^8sqrt(x)	\frac{d}{dx}(x^{8}\sqrt{x})
limit as x approaches 0 of ln(x)	\lim\:_{x\to\:0}(\ln(x))
inverse oflaplace 5/((s^3-10*s^2))	inverselaplace\:\frac{5}{(s^{3}-10\cdot\:s^{2})}
integral of (x^2+3x+1)/(x^4+5x^2+4)	\int\:\frac{x^{2}+3x+1}{x^{4}+5x^{2}+4}dx
derivative of (3x^2-10^{-10})	\frac{d}{dx}((3x^{2}-10)^{-10})
(\partial)/(\partial x)(e^xx+2ye^x)	\frac{\partial\:}{\partial\:x}(e^{x}x+2ye^{x})
limit as x approaches-2 of x^3	\lim\:_{x\to\:-2}(x^{3})
derivative of (3+8x)/(9-2x)	derivative\:\frac{3+8x}{9-2x}
derivative of f(t)=(1t^2+0t+0)^{-8}	derivative\:f(t)=(1t^{2}+0t+0)^{-8}
derivative of 4^{9^{x^2}}	\frac{d}{dx}(4^{9^{x^{2}}})
sum from n=1 to infinity of (-1)^nx^{2n}	\sum\:_{n=1}^{\infty\:}(-1)^{n}x^{2n}
inverse oflaplace 1/x*(10)/(x^2+x+10)	inverselaplace\:\frac{1}{x}\cdot\:\frac{10}{x^{2}+x+10}
derivative of sin(x^2+y^2)	\frac{d}{dx}(\sin(x^{2}+y^{2}))
area y^2=4x,x=1,x=4	area\:y^{2}=4x,x=1,x=4
limit as x approaches 0-of 2+3/x	\lim\:_{x\to\:0-}(2+\frac{3}{x})
(dy)/(dt)-4y=10sin(2t),y(0)=0	\frac{dy}{dt}-4y=10\sin(2t),y(0)=0
derivative of e^{arccsc(x})	\frac{d}{dx}(e^{\arccsc(x)})
derivative of-asin(x+bcos(x))	\frac{d}{dx}(-a\sin(x)+b\cos(x))
f(x)=4sqrt(x)	f(x)=4\sqrt{x}
(\partial)/(\partial x)(-15(3x+y)^4)	\frac{\partial\:}{\partial\:x}(-15(3x+y)^{4})
y^'=(y-1)^2	y^{\prime\:}=(y-1)^{2}
derivative of 1/(sqrt(x)(x^2-2/x))	\frac{d}{dx}(\frac{1}{\sqrt{x}}(x^{2}-\frac{2}{x}))
derivative of-(4x/((x^2-4)^2))	\frac{d}{dx}(-\frac{4x}{(x^{2}-4)^{2}})
derivative of ((x^2+6/(x^2-6))^3)	\frac{d}{dx}((\frac{x^{2}+6}{x^{2}-6})^{3})
derivative of A/(y^7)+Be^y	derivative\:\frac{A}{y^{7}}+Be^{y}
sum from n=1 to infinity of (3-2n)/(4n)	\sum\:_{n=1}^{\infty\:}\frac{3-2n}{4n}
slope of (-2,7),(2,3)	slope\:(-2,7),(2,3)
integral of sin^4(ax)	\int\:\sin^{4}(ax)dx
derivative of 10xe^{-2x}	\frac{d}{dx}(10xe^{-2x})

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