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Popular Calculus Problems

integral from 1 to 6 of pi(sqrt(x-1))^2	\int\:_{1}^{6}π(\sqrt{x-1})^{2}dx
derivative of sqrt(9-x^8)	\frac{d}{dx}(\sqrt{9-x^{8}})
integral of y^{-1/2}	\int\:y^{-\frac{1}{2}}dy
integral of (2x+1)e^{x^2+x}	\int\:(2x+1)e^{x^{2}+x}dx
limit as x approaches 1 of 5/(x-1)	\lim\:_{x\to\:1}(\frac{5}{x-1})
integral of 36+cos(x)	\int\:36+\cos(x)dx
integral of (tan(x))/(sec^2(x))	\int\:\frac{\tan(x)}{\sec^{2}(x)}dx
derivative of (2x^5+7)/(x^3)	derivative\:\frac{2x^{5}+7}{x^{3}}
tangent of ((x^2))/(x-7)	tangent\:\frac{(x^{2})}{x-7}
partialfraction x/(x^4+1)	partialfraction\:\frac{x}{x^{4}+1}
(\partial)/(\partial u)(4ucos(v))	\frac{\partial\:}{\partial\:u}(4u\cos(v))
integral of 2x^2-2x^{-1}	\int\:2x^{2}-2x^{-1}dx
(\partial)/(\partial y)(6xy-12)	\frac{\partial\:}{\partial\:y}(6xy-12)
(\partial)/(\partial x)(2x^2+3xy)	\frac{\partial\:}{\partial\:x}(2x^{2}+3xy)
integral of 1/100	\int\:\frac{1}{100}dx
derivative of \sqrt[3]{x}-3e^x	derivative\:\sqrt[3]{x}-3e^{x}
inverse oflaplace 1/((s+1)^2+5)	inverselaplace\:\frac{1}{(s+1)^{2}+5}
derivative of (h^2-2h+5)/8	derivative\:\frac{h^{2}-2h+5}{8}
derivative of 3x^{1/4}(x^3-5)	derivative\:3x^{\frac{1}{4}}(x^{3}-5)
integral from 0 to infinity of sin(5x)	\int\:_{0}^{\infty\:}\sin(5x)dx
(\partial)/(\partial x)(e^{2x}y)	\frac{\partial\:}{\partial\:x}(e^{2x}y)
(\partial)/(\partial x)(sqrt(x^2+4))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+4})
tangent of y=8x^{1/2}+4x^{3/2}+4	tangent\:y=8x^{\frac{1}{2}}+4x^{\frac{3}{2}}+4
limit as x approaches infinity of (x-cos(x))/x	\lim\:_{x\to\:\infty\:}(\frac{x-\cos(x)}{x})
integral of (-x)/((x+1)-sqrt(x+1))	\int\:\frac{-x}{(x+1)-\sqrt{x+1}}dx
derivative of y=x^2-8x-6	derivative\:y=x^{2}-8x-6
(dy)/(dx)=xe^{6x-5y}	\frac{dy}{dx}=xe^{6x-5y}
(\partial)/(\partial y)(e^{2x})	\frac{\partial\:}{\partial\:y}(e^{2x})
derivative of (2x-x^2/(sqrt(x)))	\frac{d}{dx}(\frac{2x-x^{2}}{\sqrt{x}})
2y^{''}+8y^'+80y=40cos(8t)	2y^{\prime\:\prime\:}+8y^{\prime\:}+80y=40\cos(8t)
y^{''}+5y^'+3y=0	y^{\prime\:\prime\:}+5y^{\prime\:}+3y=0
(6x+1)y^2(dy)/(dx)+3x^2+2y^3=0	(6x+1)y^{2}\frac{dy}{dx}+3x^{2}+2y^{3}=0
limit as x approaches-1+of sqrt(3x+3)-5	\lim\:_{x\to\:-1+}(\sqrt{3x+3}-5)
derivative of y=cos(3x^2)	derivative\:y=\cos(3x^{2})
limit as x approaches 3+of (3x+4)/(x-3)	\lim\:_{x\to\:3+}(\frac{3x+4}{x-3})
(\partial)/(\partial x)(((x+y))/((1+x^2)))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{(1+x^{2})})
(e^x-1)^'	(e^{x}-1)^{\prime\:}
derivative of xe^{x/2}	derivative\:xe^{\frac{x}{2}}
derivative of dcos(t)+t^2sin(t)	derivative\:d\cos(t)+t^{2}\sin(t)
limit as n approaches infinity of 6/n	\lim\:_{n\to\:\infty\:}(\frac{6}{n})
integral of 3/(7+3x)	\int\:\frac{3}{7+3x}dx
limit as x approaches 1 of-16x^2+92x	\lim\:_{x\to\:1}(-16x^{2}+92x)
integral of 1/((100-x^2)^{3/2)}	\int\:\frac{1}{(100-x^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial x)(2xsin(9x^2y))	\frac{\partial\:}{\partial\:x}(2x\sin(9x^{2}y))
integral of xsin(5x)	\int\:x\sin(5x)dx
derivative of arcsin(sqrt(sin(7x)))	\frac{d}{dx}(\arcsin(\sqrt{\sin(7x)}))
derivative of y=arcsec(1/(7t^3))	derivative\:y=\arcsec(\frac{1}{7t^{3}})
area y=\|x-3\|,y= x/2	area\:y=\left\|x-3\right\|,y=\frac{x}{2}
derivative of f(x)=tan(sec(x))	derivative\:f(x)=\tan(\sec(x))
y^{''}+14y^'+49y=0	y^{\prime\:\prime\:}+14y^{\prime\:}+49y=0
y^'=ay	y^{\prime\:}=ay
derivative of f(x)=6	derivative\:f(x)=6
integral of arccot(4y)	\int\:\arccot(4y)dy
limit as x approaches x^1 of x^2	\lim\:_{x\to\:x^{1}}(x^{2})
derivative of y=sqrt(3x-7)	derivative\:y=\sqrt{3x-7}
integral from 0 to 1 of (x^2-2x+3)	\int\:_{0}^{1}(x^{2}-2x+3)dx
integral from 0 to 1/2 of 7arccos(x)	\int\:_{0}^{\frac{1}{2}}7\arccos(x)dx
(\partial)/(\partial y)(1-xycos(piy))	\frac{\partial\:}{\partial\:y}(1-xy\cos(πy))
derivative of-ln(1-x)	derivative\:-\ln(1-x)
limit as x approaches-infinity of x/2	\lim\:_{x\to\:-\infty\:}(\frac{x}{2})
(dy)/(dx)-tan(x)y=y^3,y(0)=1	\frac{dy}{dx}-\tan(x)y=y^{3},y(0)=1
integral of 5x^4e^{x^5}	\int\:5x^{4}e^{x^{5}}dx
d/(dt)(t^3+t)	\frac{d}{dt}(t^{3}+t)
derivative of x^2*ln(x^2)	\frac{d}{dx}(x^{2}\cdot\:\ln(x^{2}))
tangent of f(x)= 1/(x+6),\at x=3	tangent\:f(x)=\frac{1}{x+6},\at\:x=3
lcm x^3,2x-15.8x^2	lcm\:x^{3},2x-15.8x^{2}
limit as x approaches infinity of (1-1/x)^{x-1}	\lim\:_{x\to\:\infty\:}((1-\frac{1}{x})^{x-1})
area sqrt(x-2),14-x,x=2	area\:\sqrt{x-2},14-x,x=2
integral from 0 to 1 of (1-sqrt(x))^2	\int\:_{0}^{1}(1-\sqrt{x})^{2}dx
integral of 9cos^2(x)tan^3(x)	\int\:9\cos^{2}(x)\tan^{3}(x)dx
derivative of 9/(5sqrt(x))	derivative\:\frac{9}{5\sqrt{x}}
integral of (3xe^{2x})/((1+2x)^2)	\int\:\frac{3xe^{2x}}{(1+2x)^{2}}dx
integral of e^{ut}	\int\:e^{ut}dt
(dy)/(dx)=xy+3x-2y-6	\frac{dy}{dx}=xy+3x-2y-6
derivative of sqrt(\|X^2-1\|)	derivative\:\sqrt{\left\|X^{2}-1\right\|}
integral of e^{ty}(-4y-1)	\int\:e^{ty}(-4y-1)dy
derivative of (4-1/(2x^2))^{-1}	derivative\:(4-\frac{1}{2x^{2}})^{-1}
tangent of f(x)=x^2-3x-4,(2,-6)	tangent\:f(x)=x^{2}-3x-4,(2,-6)
derivative of 4x^3+4x	\frac{d}{dx}(4x^{3}+4x)
(\partial)/(\partial x)((x-3y)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x-3y}{x^{2}+y^{2}})
integral of (3x-1)/(x^2-x+1)	\int\:\frac{3x-1}{x^{2}-x+1}dx
derivative of arctan(x/(1+x))	\frac{d}{dx}(\arctan(\frac{x}{1+x}))
integral of ((4x^3-3x^2-8x))/(6x)	\int\:\frac{(4x^{3}-3x^{2}-8x)}{6x}dx
limit as x approaches 0 of x^2sin(1/x)	\lim\:_{x\to\:0}(x^{2}\sin(\frac{1}{x}))
integral of 1/(-1-2x)	\int\:\frac{1}{-1-2x}dx
derivative of (5x^6+2x^3^4)	\frac{d}{dx}((5x^{6}+2x^{3})^{4})
inverse oflaplace 1/((s+1)^5)	inverselaplace\:\frac{1}{(s+1)^{5}}
sum from n=0 to infinity of 1/(2^{n+1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{n+1}}
integral of (3x^2-2x)^3	\int\:(3x^{2}-2x)^{3}dx
(d^2y)/(dx^2)=x^2	\frac{d^{2}y}{dx^{2}}=x^{2}
derivative of 4sqrt(3x^2+9)	\frac{d}{dx}(4\sqrt{3x^{2}+9})
integral from 0 to ln(sqrt(3 of))(4e^x)/(1+e^{2x)}	\int\:_{0}^{\ln(\sqrt{3})}\frac{4e^{x}}{1+e^{2x}}dx
derivative of x(9^{-2x})	derivative\:x(9^{-2x})
derivative of y=x+e^x-1/x	derivative\:y=x+e^{x}-\frac{1}{x}
derivative of (cos(x))/(2+sin(x))	derivative\:\frac{\cos(x)}{2+\sin(x)}
limit as x approaches 0 of (9sin(x))/x	\lim\:_{x\to\:0}(\frac{9\sin(x)}{x})
integral of (sqrt(x))/(x-25)	\int\:\frac{\sqrt{x}}{x-25}dx
integral of 3tsqrt(t^2+8)	\int\:3t\sqrt{t^{2}+8}dt
(\partial)/(\partial x)(cos^6(y^7x^8))	\frac{\partial\:}{\partial\:x}(\cos^{6}(y^{7}x^{8}))
limit as x approaches 0 of x^3sin(x^1)	\lim\:_{x\to\:0}(x^{3}\sin(x^{1}))

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