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Popular Calculus Problems

integral of 1/(xsqrt(x^2+9))	\int\:\frac{1}{x\sqrt{x^{2}+9}}dx
integral of 4/((x+1))	\int\:\frac{4}{(x+1)}dx
(d^2y)/(dt^2)+5(dy)/(dt)+6y=3cos(2t)	\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=3\cos(2t)
inverse oflaplace 3/((s+2))	inverselaplace\:\frac{3}{(s+2)}
y^{''}+2y^'+2y=e^{-t}cos(t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=e^{-t}\cos(t)
derivative of ln(e^{sin(x}*x^{cos(x)}))	\frac{d}{dx}(\ln(e^{\sin(x)}\cdot\:x^{\cos(x)}))
limit as x approaches-1 of x^3+3x^2-2x-3	\lim\:_{x\to\:-1}(x^{3}+3x^{2}-2x-3)
ty^'+4y=t^3,y(2)=4	ty^{\prime\:}+4y=t^{3},y(2)=4
derivative of w/(sqrt(1-4x^2))	\frac{d}{dx}(\frac{w}{\sqrt{1-4x^{2}}})
derivative of 2t^{-1/4}+2ln(t)+ln(5)	derivative\:2t^{-\frac{1}{4}}+2\ln(t)+\ln(5)
y^{''}-y^'+0.25y=0	y^{\prime\:\prime\:}-y^{\prime\:}+0.25y=0
integral of e^{4x}sin(bx)	\int\:e^{4x}\sin(bx)dx
derivative of f(x)=x+9	derivative\:f(x)=x+9
integral of 5x^{3/2}	\int\:5x^{\frac{3}{2}}dx
limit as x approaches infinity of (x)(e^{1/x})	\lim\:_{x\to\:\infty\:}((x)(e^{\frac{1}{x}}))
limit as t approaches 1 of sqrt(t+4)	\lim\:_{t\to\:1}(\sqrt{t+4})
limit as x approaches 5 of-(x-3)^2	\lim\:_{x\to\:5}(-(x-3)^{2})
d/(dt)(1.1t+6.3t^3)	\frac{d}{dt}(1.1t+6.3t^{3})
limit as x approaches infinity of ((x+1}{x+2})^{\frac{-4x)/5}	\lim\:_{x\to\:\infty\:}((\frac{x+1}{x+2})^{\frac{-4x}{5}})
derivative of f(x)=(x^3+7)/x	derivative\:f(x)=\frac{x^{3}+7}{x}
integral of 3/(x^5)	\int\:\frac{3}{x^{5}}dx
integral of ((16x^2))/((sqrt(x^2+9))^5)	\int\:\frac{(16x^{2})}{(\sqrt{x^{2}+9})^{5}}dx
integral of (x^2-x+1)/(x^3)	\int\:\frac{x^{2}-x+1}{x^{3}}dx
derivative of-5sin(xcos(x))	\frac{d}{dx}(-5\sin(x)\cos(x))
derivative of f(x)=8x^7e^x+e^xx^8	derivative\:f(x)=8x^{7}e^{x}+e^{x}x^{8}
derivative of 2sinh(2x)	\frac{d}{dx}(2\sinh(2x))
sum from n=1 to infinity of n^3sin(1/n)	\sum\:_{n=1}^{\infty\:}n^{3}\sin(\frac{1}{n})
derivative of f(x)= 9/(x^2)	derivative\:f(x)=\frac{9}{x^{2}}
-9y^{''}+36y=0,y(1)=1,y^'(-1)=-2	-9y^{\prime\:\prime\:}+36y=0,y(1)=1,y^{\prime\:}(-1)=-2
limit as x approaches infinity of (-2)/0	\lim\:_{x\to\:\infty\:}(\frac{-2}{0})
limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)}	\lim\:_{x\to\:\infty\:}(\frac{(\sin^{2}(x))}{x+e^{-x}})
derivative of y=sqrt(x/(x+9))	derivative\:y=\sqrt{\frac{x}{x+9}}
inverse oflaplace (s+1)/(s^2+3s+2)	inverselaplace\:\frac{s+1}{s^{2}+3s+2}
(\partial)/(\partial y)(e^xln(xy))	\frac{\partial\:}{\partial\:y}(e^{x}\ln(xy))
integral of e^{x/(10)}	\int\:e^{\frac{x}{10}}dx
integral of 3x^2+3x^2ln(y)	\int\:3x^{2}+3x^{2}\ln(y)dx
integral from 1 to 4 of (6x+sqrt(x))	\int\:_{1}^{4}(6x+\sqrt{x})dx
derivative of (cos(x*e^x)/(tan(x)))	\frac{d}{dx}(\frac{\cos(x)\cdot\:e^{x}}{\tan(x)})
integral of cot^2(5x)csc(5x)	\int\:\cot^{2}(5x)\csc(5x)dx
derivative of arcsinh(sqrt(1-x^2))	\frac{d}{dx}(\arcsinh(\sqrt{1-x^{2}}))
derivative of e^{-2t}cos(x)	\frac{d}{dx}(e^{-2t}\cos(x))
integral of a+bx	\int\:a+bxdx
limit as x approaches 0 of (3\|x\|)/(x^2)	\lim\:_{x\to\:0}(\frac{3\left\|x\right\|}{x^{2}})
integral of ((65x+7))/((8x+1)(x-1))	\int\:\frac{(65x+7)}{(8x+1)(x-1)}dx
integral of (10)/(e^{x/2)}	\int\:\frac{10}{e^{\frac{x}{2}}}dx
integral of (tan^3(x))/(sec(x))	\int\:\frac{\tan^{3}(x)}{\sec(x)}dx
(\partial)/(\partial y)(x^4y-x^2y^3)	\frac{\partial\:}{\partial\:y}(x^{4}y-x^{2}y^{3})
(\partial)/(\partial x)(1-(x^2+y^2)^{1/7})	\frac{\partial\:}{\partial\:x}(1-(x^{2}+y^{2})^{\frac{1}{7}})
limit as x approaches 3-of e^{7/((x-3))}	\lim\:_{x\to\:3-}(e^{\frac{7}{(x-3)}})
derivative of (e^{x^2}/(2x))	\frac{d}{dx}(\frac{e^{x^{2}}}{2x})
integral from 1 to 2 of (x-sqrt(x))	\int\:_{1}^{2}(x-\sqrt{x})dx
derivative of e^{-x^2-y^2}	\frac{d}{dx}(e^{-x^{2}-y^{2}})
integral of arccsc(x)	\int\:\arccsc(x)dx
sum from n=1 to infinity of (x^n)/(n+5)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{n+5}
(\partial)/(\partial x)(7xy^4+2)	\frac{\partial\:}{\partial\:x}(7xy^{4}+2)
integral of 1/((x+1)(x^2+25))	\int\:\frac{1}{(x+1)(x^{2}+25)}dx
integral of (x^{3/2}+8)^6sqrt(x)	\int\:(x^{\frac{3}{2}}+8)^{6}\sqrt{x}dx
sum from n=1 to infinity of (-10/11)^n	\sum\:_{n=1}^{\infty\:}(-\frac{10}{11})^{n}
derivative of x/(y^2-y/(x^2))	\frac{d}{dx}(\frac{x}{y^{2}}-\frac{y}{x^{2}})
tangent of f(x)= 1/(1+x^2),\at x=-1	tangent\:f(x)=\frac{1}{1+x^{2}},\at\:x=-1
(\partial)/(\partial θ)(nln(2θ))	\frac{\partial\:}{\partial\:θ}(n\ln(2θ))
integral of (50x)/(sec(5x^2+5))	\int\:\frac{50x}{\sec(5x^{2}+5)}dx
limit as x approaches 0 of ((8^x-5^x))/x	\lim\:_{x\to\:0}(\frac{(8^{x}-5^{x})}{x})
derivative of 1/(e^{x^2)}	derivative\:\frac{1}{e^{x^{2}}}
y^'=xy^3-xy	y^{\prime\:}=xy^{3}-xy
taylor x^5-x^3+x,1	taylor\:x^{5}-x^{3}+x,1
(dy)/(dx)=cos(3x)	\frac{dy}{dx}=\cos(3x)
(\partial)/(\partial x)(2x^3y+8y^3)	\frac{\partial\:}{\partial\:x}(2x^{3}y+8y^{3})
integral of 4-x^2	\int\:4-x^{2}dx
integral of 1/(tsqrt(t))	\int\:\frac{1}{t\sqrt{t}}dt
integral of x/((x^2-6x+10)^2)	\int\:\frac{x}{(x^{2}-6x+10)^{2}}dx
derivative of e^{-2ix}	\frac{d}{dx}(e^{-2ix})
(\partial)/(\partial x)((6x)/((x^2+9)))	\frac{\partial\:}{\partial\:x}(\frac{6x}{(x^{2}+9)})
sum from n=0 to infinity of n/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n}{2^{n}}
tangent of 9e^x+x	tangent\:9e^{x}+x
limit as x approaches-4 of (x^2-2)/(4-x)	\lim\:_{x\to\:-4}(\frac{x^{2}-2}{4-x})
derivative of ln(5x^4)	derivative\:\ln(5x^{4})
integral of (x^2)/4	\int\:\frac{x^{2}}{4}dx
(\partial)/(\partial x)((e^{2y}-ycos(xy))dx)	\frac{\partial\:}{\partial\:x}((e^{2y}-y\cos(xy))dx)
integral of e^xsqrt(1+e^{2x)}	\int\:e^{x}\sqrt{1+e^{2x}}dx
derivative of y=x^{4^x}	derivative\:y=x^{4^{x}}
integral of 9xe^{5x^2}	\int\:9xe^{5x^{2}}dx
derivative of A(e^x+e^xx)	\frac{d}{dx}(A(e^{x}+e^{x}x))
tangent of x^2+xy+2y^2=4,(-2,1)	tangent\:x^{2}+xy+2y^{2}=4,(-2,1)
9y^{''}+6y^'+y=0,y(-3)=-2,y^'(1)=-1	9y^{\prime\:\prime\:}+6y^{\prime\:}+y=0,y(-3)=-2,y^{\prime\:}(1)=-1
derivative of x^2-xy	\frac{d}{dx}(x^{2}-xy)
y^'=1+x^2+y^2+x^2y^2	y^{\prime\:}=1+x^{2}+y^{2}+x^{2}y^{2}
integral from 0 to 1 of y/(e^{2y)}	\int\:_{0}^{1}\frac{y}{e^{2y}}dy
(\partial)/(\partial y)(xy^3z^2)	\frac{\partial\:}{\partial\:y}(xy^{3}z^{2})
derivative of x^2-2/(x^2)	\frac{d}{dx}(x^{2}-\frac{2}{x^{2}})
(\partial)/(\partial x)(x*Y(x))	\frac{\partial\:}{\partial\:x}(x\cdot\:Y(x))
slope ofintercept (-7,-4),(-2,3)	slopeintercept\:(-7,-4),(-2,3)
limit as x approaches infinity of 4-3/x	\lim\:_{x\to\:\infty\:}(4-\frac{3}{x})
area 5-x^2,sin(x),-2.385,2.025	area\:5-x^{2},\sin(x),-2.385,2.025
derivative of (4-x^2)^5	derivative\:(4-x^{2})^{5}
integral of (e^x+1/(3x))	\int\:(e^{x}+\frac{1}{3x})dx
limit as x approaches-4+of [x]	\lim\:_{x\to\:-4+}([x])
integral of (x^2sqrt(x^2+1))	\int\:(x^{2}\sqrt{x^{2}+1})dx
derivative of x^4-2x^3	derivative\:x^{4}-2x^{3}
derivative of (2/5 x)^9	derivative\:(\frac{2}{5}x)^{9}

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