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Popular Calculus Problems

limit as x approaches infinity of x^{10}	\lim\:_{x\to\:\infty\:}(x^{10})
integral of x^2ln(x+1)	\int\:x^{2}\ln(x+1)dx
derivative of sqrt(e^{2x)+4e^{-4x}+1}	\frac{d}{dx}(\sqrt{e^{2x}+4e^{-4x}+1})
integral from 1 to 2 of (13)/(x^3+4x)	\int\:_{1}^{2}\frac{13}{x^{3}+4x}dx
tangent of f(x)=xsqrt(x),(16,64)	tangent\:f(x)=x\sqrt{x},(16,64)
derivative of e^xcos(3x-3e^xsin(3x))	\frac{d}{dx}(e^{x}\cos(3x)-3e^{x}\sin(3x))
integral from 0 to 5 of pi(x^2)	\int\:_{0}^{5}π(x^{2})dx
integral of 1/(4x^2+10x+5)	\int\:\frac{1}{4x^{2}+10x+5}dx
1/y (dy)/(dx)= 2/x	\frac{1}{y}\frac{dy}{dx}=\frac{2}{x}
integral of u^9	\int\:u^{9}du
integral of 1/(8-2x-x^2)	\int\:\frac{1}{8-2x-x^{2}}dx
derivative of e^{x^2+2x+1}	\frac{d}{dx}(e^{x^{2}+2x+1})
limit as x approaches 4 of sqrt(x+5)	\lim\:_{x\to\:4}(\sqrt{x+5})
tangent of f(x)=-2x^2	tangent\:f(x)=-2x^{2}
(y^2+yx)dx+(-x^2)dy=0	(y^{2}+yx)dx+(-x^{2})dy=0
y^'=(y^2+4xsqrt(x^2+y^2))/(xy)	y^{\prime\:}=\frac{y^{2}+4x\sqrt{x^{2}+y^{2}}}{xy}
derivative of ln(4x+1)	derivative\:\ln(4x+1)
tangent of 3x^2-4x+1	tangent\:3x^{2}-4x+1
derivative of (8(3x^4+5)^3)	\frac{d}{dx}((8(3x)^{4}+5)^{3})
integral of (20x^2+x+45)/(x(4x^2+9))	\int\:\frac{20x^{2}+x+45}{x(4x^{2}+9)}dx
derivative of y= 4/((sqrt(2x))^3)	derivative\:y=\frac{4}{(\sqrt{2x})^{3}}
integral of (-7-7tan^2(θ))	\int\:(-7-7\tan^{2}(θ))dθ
(dP)/(dx)=0.05P(1-P/(2000))	\frac{dP}{dx}=0.05P(1-\frac{P}{2000})
(\partial)/(\partial x)(5x+8y+10z)	\frac{\partial\:}{\partial\:x}(5x+8y+10z)
f^'(x)=(x^2)/((9+4x))	f^{\prime\:}(x)=\frac{x^{2}}{(9+4x)}
y^3dx-xy^2dy+x^3dx=0	y^{3}dx-xy^{2}dy+x^{3}dx=0
derivative of 2pix^2	\frac{d}{dx}(2πx^{2})
tangent of y=xsqrt(x),(4,8)	tangent\:y=x\sqrt{x},(4,8)
(\partial)/(\partial t)(2cos(t)+8x^2)	\frac{\partial\:}{\partial\:t}(2\cos(t)+8x^{2})
derivative of 3cos(x-2e^{2x})	\frac{d}{dx}(3\cos(x)-2e^{2x})
tangent of f(x)=x^3-2x+1,\at x=-1	tangent\:f(x)=x^{3}-2x+1,\at\:x=-1
(e^x-e^{-x})(dy)/(dx)=y^2	(e^{x}-e^{-x})\frac{dy}{dx}=y^{2}
(\partial)/(\partial x)(-10x+7y^5)	\frac{\partial\:}{\partial\:x}(-10x+7y^{5})
derivative of 1/(4x^3-6/(5x^4))	\frac{d}{dx}(\frac{1}{4x^{3}}-\frac{6}{5x^{4}})
(dy)/(dx)=((2y+5)/(8x+7))^2	\frac{dy}{dx}=(\frac{2y+5}{8x+7})^{2}
y^'-3y=3e^{4t}	y^{\prime\:}-3y=3e^{4t}
2x+y+(x+2y)*y^'=0	2x+y+(x+2y)\cdot\:y^{\prime\:}=0
tangent of f(x)=4x^2+5x-5	tangent\:f(x)=4x^{2}+5x-5
sum from n=1 to infinity}((-1)^{n+1 of)/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n+1}}{n^{5}}
tangent of 3x-2sqrt(x)	tangent\:3x-2\sqrt{x}
sum from n=1 to infinity of 1/(cos(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{\cos(n)}
integral of-6sin(2x)	\int\:-6\sin(2x)dx
integral from 0 to 3 of xsqrt(11-x^2)	\int\:_{0}^{3}x\sqrt{11-x^{2}}dx
derivative of (2/5 ^x)	\frac{d}{dx}((\frac{2}{5})^{x})
integral of 1/(1+4x^2)	\int\:\frac{1}{1+4x^{2}}dx
(x+y+4)dx+(2x+2y+1)dy=0	(x+y+4)dx+(2x+2y+1)dy=0
(dy)/(dx)(sqrt(25-x^2))+5xy=0	\frac{dy}{dx}(\sqrt{25-x^{2}})+5xy=0
derivative of ((1-x^2)/(x^2))	\frac{d}{dx}(\frac{(1-x)^{2}}{x^{2}})
y^'=yxe^{x^2}-y	y^{\prime\:}=yxe^{x^{2}}-y
limit as x approaches 0-of x^2ln(x)	\lim\:_{x\to\:0-}(x^{2}\ln(x))
y^'-x^2=2x^2y	y^{\prime\:}-x^{2}=2x^{2}y
derivative of (x^2/(10+x))	\frac{d}{dx}(\frac{x^{2}}{10+x})
derivative of sqrt(18x)	derivative\:\sqrt{18x}
tangent of f(x)=5x-4x^2,(-2,-26)	tangent\:f(x)=5x-4x^{2},(-2,-26)
integral of 3sqrt(x+4)	\int\:3\sqrt{x+4}dx
integral of sin^2(x)cos(x)	\int\:\sin^{2}(x)\cos(x)dx
integral of (x+6)/(x+1)	\int\:\frac{x+6}{x+1}dx
integral of (x+1)/(12)	\int\:\frac{x+1}{12}dx
integral of 3x^2	\int\:3x^{2}dx
integral from 0 to 8 of 2pix(x^{2/3})	\int\:_{0}^{8}2πx(x^{\frac{2}{3}})dx
derivative of 4/3 x^3	\frac{d}{dx}(\frac{4}{3}x^{3})
integral from-3 to 0 of 4x^{1/3}	\int\:_{-3}^{0}4x^{\frac{1}{3}}dx
integral of (x^3)/(\sqrt[5]{x^2+7)}	\int\:\frac{x^{3}}{\sqrt[5]{x^{2}+7}}dx
integral of x^3sqrt(25-x^2)	\int\:x^{3}\sqrt{25-x^{2}}dx
inverse oflaplace 1/((s-2)^2)	inverselaplace\:\frac{1}{(s-2)^{2}}
derivative of 1-\|x-1\|	\frac{d}{dx}(1-\left\|x-1\right\|)
integral from-1 to 1 of (4-4x^2)^2	\int\:_{-1}^{1}(4-4x^{2})^{2}dx
(\partial)/(\partial x)(tan(u/v))	\frac{\partial\:}{\partial\:x}(\tan(\frac{u}{v}))
derivative of (x+y^2)	\frac{d}{dx}((x+y)^{2})
integral from 0 to 1 of sqrt(1+9x^2)	\int\:_{0}^{1}\sqrt{1+9x^{2}}dx
integral of-1/(cos^2(x))	\int\:-\frac{1}{\cos^{2}(x)}dx
derivative of (6-2x/(x^2-4))	\frac{d}{dx}(\frac{6-2x}{x^{2}-4})
derivative of d-d/(x^2-ax-b)	\frac{d}{dx}(d-\frac{d}{x^{2}}-ax-b)
derivative of (1+cos(2x)/2)	\frac{d}{dx}(\frac{1+\cos(2x)}{2})
integral of ln\|e^{xy}cos(x)\|	\int\:\ln\left\|e^{xy}\cos(x)\right\|dy
integral of t*ln(t+1)	\int\:t\cdot\:\ln(t+1)dt
derivative of 3/(x+9)	\frac{d}{dx}(\frac{3}{x+9})
derivative of-7z^4+z^2-25	derivative\:-7z^{4}+z^{2}-25
(\partial)/(\partial x)(((x^2))/(y+3))	\frac{\partial\:}{\partial\:x}(\frac{(x^{2})}{y+3})
limit as x approaches 4 of (\|x\|-4)/(x-4)	\lim\:_{x\to\:4}(\frac{\left\|x\right\|-4}{x-4})
(\partial)/(\partial z)(xe^{-y}-z)	\frac{\partial\:}{\partial\:z}(xe^{-y}-z)
derivative of f(x)=cos(arctan(x))	derivative\:f(x)=\cos(\arctan(x))
limit as x approaches 0 of ((x^2)/2)-x	\lim\:_{x\to\:0}((\frac{x^{2}}{2})-x)
derivative of (sqrt(s)-2)/(sqrt(s)+4)	derivative\:\frac{\sqrt{s}-2}{\sqrt{s}+4}
sum from n=1 to infinity of 2(3/4)^n	\sum\:_{n=1}^{\infty\:}2(\frac{3}{4})^{n}
lcm (sec^2(x))/4 ,4cos^2(x)	lcm\:\frac{\sec^{2}(x)}{4},4\cos^{2}(x)
limit as x approaches-2+of ((x+3))/(x+2)	\lim\:_{x\to\:-2+}(\frac{(x+3)}{x+2})
integral of 1/(x^2sqrt(4x^2-36))	\int\:\frac{1}{x^{2}\sqrt{4x^{2}-36}}dx
integral of (x+5)sqrt(5-x)	\int\:(x+5)\sqrt{5-x}dx
derivative of f(x)=8sqrt(x)sin(x)	derivative\:f(x)=8\sqrt{x}\sin(x)
derivative of ln(e^2)	\frac{d}{dx}(\ln(e^{2}))
integral from 0 to 3 of (2x+1)	\int\:_{0}^{3}(2x+1)dx
y^{''}+16y=16sin(4t)	y^{\prime\:\prime\:}+16y=16\sin(4t)
integral of 1/(cos^2(2y))	\int\:\frac{1}{\cos^{2}(2y)}dy
derivative of f(x)=14(2x+5)^6	derivative\:f(x)=14(2x+5)^{6}
(\partial}{\partial y}(\frac{y^3)/x)	\frac{\partial\:}{\partial\:y}(\frac{y^{3}}{x})
derivative of t^8cos(t)	derivative\:t^{8}\cos(t)
laplacetransform t^2*e^{-,\at}	laplacetransform\:t^{2}\cdot\:e^{-,\at\:}
tangent of f(x)=x(4-x)^3,\at x=2	tangent\:f(x)=x(4-x)^{3},\at\:x=2
laplacetransform f(t)=3sin(4t)-2e^{2t}	laplacetransform\:f(t)=3\sin(4t)-2e^{2t}

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