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Popular Calculus Problems

integral of 1/(pisqrt(x(1-x)))	\int\:\frac{1}{π\sqrt{x(1-x)}}dx
derivative of cos(2-7x)	\frac{d}{dx}(\cos(2-7x))
derivative of f(x)=(2x-8)^4(x^2+x+1)^5	derivative\:f(x)=(2x-8)^{4}(x^{2}+x+1)^{5}
integral from 0 to infinity of te^{-st}	\int\:_{0}^{\infty\:}te^{-st}dt
integral from 0 to 3 of e^xsin(x)	\int\:_{0}^{3}e^{x}\sin(x)dx
limit as h approaches 0 of 1/(h+1)	\lim\:_{h\to\:0}(\frac{1}{h+1})
integral of x^{-3}(x+1)	\int\:x^{-3}(x+1)dx
integral from 0 to 1 of 8^{2x}	\int\:_{0}^{1}8^{2x}dx
derivative of 5xsin(x^2)	derivative\:5x\sin(x^{2})
integral of (e^{sqrt(x)})/(sqrt(x))	\int\:\frac{e^{\sqrt{x}}}{\sqrt{x}}dx
derivative of f(x)=8xe^x-8e^x	derivative\:f(x)=8xe^{x}-8e^{x}
derivative of x4^x	\frac{d}{dx}(x4^{x})
derivative of x^{13}	derivative\:x^{13}
implicit (dy)/(dx),(7xy+3)^2=14y	implicit\:\frac{dy}{dx},(7xy+3)^{2}=14y
integral of 729x^2cos(9x)	\int\:729x^{2}\cos(9x)dx
taylor ln(cos(x)+sin(x))	taylor\:\ln(\cos(x)+\sin(x))
derivative of e^x(x+1)	derivative\:e^{x}(x+1)
integral of e^{-5}	\int\:e^{-5}dx
derivative of sqrt(x^2-y^2)	\frac{d}{dx}(\sqrt{x^{2}-y^{2}})
integral of 2/(2x-3)	\int\:\frac{2}{2x-3}dx
(dy)/(dx)=2y+x^2+5	\frac{dy}{dx}=2y+x^{2}+5
(dy)/(dx)+(4/x)y=4x+9	\frac{dy}{dx}+(\frac{4}{x})y=4x+9
laplacetransform 2e^{4t}	laplacetransform\:2e^{4t}
tangent of x^4	tangent\:x^{4}
integral of 2xe^{2x}	\int\:2xe^{2x}dx
integral from 1 to 2 of (x^5+5x^8)/(x^4)	\int\:_{1}^{2}\frac{x^{5}+5x^{8}}{x^{4}}dx
derivative of x^{1/3}+2x	\frac{d}{dx}(x^{\frac{1}{3}}+2x)
integral from 0 to 9 of sqrt(x)	\int\:_{0}^{9}\sqrt{x}dx
y^{''}+4y=t-2sin(2t)	y^{\prime\:\prime\:}+4y=t-2\sin(2t)
derivative of ((sqrt(x)-1)/(sqrt(x)+1))	\frac{d}{dx}(\frac{(\sqrt{x}-1)}{\sqrt{x}+1})
limit as x approaches infinity of (sqrt(x^2-9))/(2x-6)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{x^{2}-9}}{2x-6})
y^{''}-8y^'+16y=e^{4x}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=e^{4x}
derivative of 4x^2+6x	\frac{d}{dx}(4x^{2}+6x)
(\partial)/(\partial s)(sqrt(s^6+t^6))	\frac{\partial\:}{\partial\:s}(\sqrt{s^{6}+t^{6}})
(df)/(dx)+2f=fx^3	\frac{df}{dx}+2f=fx^{3}
sum from n=0 to infinity of (1/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{3})^{n}
area 2x^2+3,x,(-1,2)	area\:2x^{2}+3,x,(-1,2)
integral from-2 to 2 of pi(4-x^2)	\int\:_{-2}^{2}π(4-x^{2})dx
(y+4)*y^'=2xy+4y,y(2)=1	(y+4)\cdot\:y^{\prime\:}=2xy+4y,y(2)=1
limit as x approaches+9-of (-7)/((x+9))	\lim\:_{x\to\:+9-}(\frac{-7}{(x+9)})
integral of sin^3(t)cos(t)	\int\:\sin^{3}(t)\cos(t)dt
derivative of 1/3 (y^2+2)^{3/2}	derivative\:\frac{1}{3}(y^{2}+2)^{\frac{3}{2}}
derivative of ln(2ln(x))	\frac{d}{dx}(\ln(2\ln(x)))
derivative of (3x+1^4)	\frac{d}{dx}((3x+1)^{4})
derivative of 1/(3x)	derivative\:\frac{1}{3x}
derivative of (x-3/(x+3))	\frac{d}{dx}(\frac{x-3}{x+3})
integral from 0 to 1 of (37)/(4y-1)	\int\:_{0}^{1}\frac{37}{4y-1}dy
integral from 0 to sqrt(3 of)arctan(x)	\int\:_{0}^{\sqrt{3}}\arctan(x)dx
(\partial)/(\partial x)(-sin(x)-sin(2y))	\frac{\partial\:}{\partial\:x}(-\sin(x)-\sin(2y))
derivative of f(x)=(x^2)/(7+sqrt(x))	derivative\:f(x)=\frac{x^{2}}{7+\sqrt{x}}
xy^'-2y=2yx^2	xy^{\prime\:}-2y=2yx^{2}
limit as x approaches 0 of x*cot(2x)	\lim\:_{x\to\:0}(x\cdot\:\cot(2x))
slope of y=x^2-2x-3,(2,-3)	slope\:y=x^{2}-2x-3,(2,-3)
(\partial)/(\partial x)(sqrt(xy))	\frac{\partial\:}{\partial\:x}(\sqrt{xy})
derivative of (x/(y^2)-(y/(x^2)))	\frac{d}{dx}((\frac{x}{y^{2}})-(\frac{y}{x^{2}}))
inverse oflaplace 1/(s+1)*1/s	inverselaplace\:\frac{1}{s+1}\cdot\:\frac{1}{s}
sum from n=0 to infinity of n(1/4)^n	\sum\:_{n=0}^{\infty\:}n(\frac{1}{4})^{n}
limit as x approaches 0 of-6+6x^3	\lim\:_{x\to\:0}(-6+6x^{3})
y=3^2+3	y=3^{2}+3
integral of e^{2ax}	\int\:e^{2ax}dx
integral from-5 to 4 of t^2	\int\:_{-5}^{4}t^{2}dt
integral of ((sqrt(x^2-4)))/x	\int\:\frac{(\sqrt{x^{2}-4})}{x}dx
derivative of (8x^2+8x+8/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+8x+8}{\sqrt{x}})
derivative of x^3sinh^2(x+cosh^2(x^3))	\frac{d}{dx}(x^{3}\sinh^{2}(x)+\cosh^{2}(x^{3}))
area x=9,x=y^2	area\:x=9,x=y^{2}
integral of 12x+12	\int\:12x+12dx
integral of (e^{4x}+4e^x+8)/(e^x)	\int\:\frac{e^{4x}+4e^{x}+8}{e^{x}}dx
integral of x^5e^{-x}	\int\:x^{5}e^{-x}dx
tangent of f(x)= 5/x ,\at x=2	tangent\:f(x)=\frac{5}{x},\at\:x=2
derivative of e^{2x}sqrt(x+1)	\frac{d}{dx}(e^{2x}\sqrt{x+1})
integral of 7-1/(7x^2)	\int\:7-\frac{1}{7x^{2}}dx
integral of (x^6)/((8-x^7)^2)	\int\:\frac{x^{6}}{(8-x^{7})^{2}}dx
limit as x approaches infinity of 1+x	\lim\:_{x\to\:\infty\:}(1+x)
integral of 19e^x	\int\:19e^{x}dx
integral of xcos^2(8x)	\int\:x\cos^{2}(8x)dx
(dy}{dx}=\frac{x+2)/y	\frac{dy}{dx}=\frac{x+2}{y}
integral of 1/(7x+3)	\int\:\frac{1}{7x+3}dx
derivative of-2tan(x)	\frac{d}{dx}(-2\tan(x))
integral of (4x-1)^3	\int\:(4x-1)^{3}dx
limit as x approaches 3+of 1/(6-2x)	\lim\:_{x\to\:3+}(\frac{1}{6-2x})
integral of (x^2)/(x^4-6x^2-27)	\int\:\frac{x^{2}}{x^{4}-6x^{2}-27}dx
yy^'+36x=0	yy^{\prime\:}+36x=0
integral of (20x^3-40x^2+9)/(x^2-2x)	\int\:\frac{20x^{3}-40x^{2}+9}{x^{2}-2x}dx
(\partial)/(\partial z)(e^x)	\frac{\partial\:}{\partial\:z}(e^{x})
y^3-(6x+2)+3xy^2y^'=0	y^{3}-(6x+2)+3xy^{2}y^{\prime\:}=0
tangent of (x^3-4x)^8	tangent\:(x^{3}-4x)^{8}
(\partial)/(\partial x)(sqrt(x^2+y^2-1))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}-1})
derivative of f(x)=(x^3)/((x^2+4)^2)	derivative\:f(x)=\frac{x^{3}}{(x^{2}+4)^{2}}
y^'-(3y)/x =x	y^{\prime\:}-\frac{3y}{x}=x
derivative of sin(x^2)+((1-x))/(1+x)	derivative\:\sin(x^{2})+\frac{(1-x)}{1+x}
derivative of ((x^2-1)/(x^2+x+1))	\frac{d}{dx}(\frac{(x^{2}-1)}{x^{2}+x+1})
sum from k=0 to infinity of 5x^k	\sum\:_{k=0}^{\infty\:}5x^{k}
derivative of sqrt(2x-9)	\frac{d}{dx}(\sqrt{2x-9})
integral of (x-1)^{1/2}	\int\:(x-1)^{\frac{1}{2}}dx
integral of sin(y)cosh(x)	\int\:\sin(y)\cosh(x)dy
integral of (-(x^2-1)(6x^2+6))/(x^2+1)	\int\:\frac{-(x^{2}-1)(6x^{2}+6)}{x^{2}+1}dx
integral of 1/(0.15x+20)	\int\:\frac{1}{0.15x+20}dx
f(n)=2^n	f(n)=2^{n}
integral of 9xcos(2x)	\int\:9x\cos(2x)dx
area y=x^2-1,(-1,1)	area\:y=x^{2}-1,(-1,1)

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