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Popular Calculus Problems

(\partial)/(\partial y)(ye^{xy}+sin(y))	\frac{\partial\:}{\partial\:y}(ye^{xy}+\sin(y))
integral of e^{ax}sin(bx)	\int\:e^{ax}\sin(bx)dx
(\partial)/(\partial x)(e^{-x}sin(y)z)	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(y)z)
sum from n=1 to infinity of (3n)/(6n+13)	\sum\:_{n=1}^{\infty\:}\frac{3n}{6n+13}
integral of 1/(xln^2(x))	\int\:\frac{1}{x\ln^{2}(x)}dx
f(x)=cos(4x+1)	f(x)=\cos(4x+1)
integral from-2 to 0 of (4-x)	\int\:_{-2}^{0}(4-x)dx
(\partial)/(\partial x)((e^x)/(1+e^x))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{1+e^{x}})
integral of 1/((x-1)(x+2)(x+3))	\int\:\frac{1}{(x-1)(x+2)(x+3)}dx
(\partial)/(\partial x)(sin(pi(4x-4y)))	\frac{\partial\:}{\partial\:x}(\sin(π(4x-4y)))
simplify 2/(sqrt(x))	simplify\:\frac{2}{\sqrt{x}}
derivative of ((x^3)/(x^8+7))^2	derivative\:(\frac{x^{3}}{x^{8}+7})^{2}
limit as h approaches 0 of h^4cos(3/h)	\lim\:_{h\to\:0}(h^{4}\cos(\frac{3}{h}))
(\partial)/(\partial x)(8e^{x^8y})	\frac{\partial\:}{\partial\:x}(8e^{x^{8}y})
integral of (sec^3(x))/(tan^4(x))	\int\:\frac{\sec^{3}(x)}{\tan^{4}(x)}dx
d/(dy)(sqrt(x^2+y^2))	\frac{d}{dy}(\sqrt{x^{2}+y^{2}})
derivative of x/(x+10)	\frac{d}{dx}(\frac{x}{x+10})
integral of ((x+5)/(x^2+11x+18))	\int\:(\frac{x+5}{x^{2}+11x+18})dx
limit as x approaches 0 of sqrt(1+x)	\lim\:_{x\to\:0}(\sqrt{1+x})
integral of+(arcsin(x))^2	\int\:+(\arcsin(x))^{2}dx
integral of (x^2)/(x+7)	\int\:\frac{x^{2}}{x+7}dx
y^{''}-2y^'-15y=e^{3x}cos(2x)	y^{\prime\:\prime\:}-2y^{\prime\:}-15y=e^{3x}\cos(2x)
derivative of 2x-7	\frac{d}{dx}(2x-7)
integral of cos^5(t)	\int\:\cos^{5}(t)dt
taylor cos(pi-6x)	taylor\:\cos(π-6x)
derivative of y=2sin(x)+ce^{-x}cos(x)	derivative\:y=2\sin(x)+ce^{-x}\cos(x)
18y^{''}+9y^'-2y=0	18y^{\prime\:\prime\:}+9y^{\prime\:}-2y=0
y^'=3x^2+1	y^{\prime\:}=3x^{2}+1
inverse oflaplace (5s-2)/(7s^2-s-11)	inverselaplace\:\frac{5s-2}{7s^{2}-s-11}
limit as x approaches-infinity of x-2	\lim\:_{x\to\:-\infty\:}(x-2)
integral of (x-6)^2(x+8)	\int\:(x-6)^{2}(x+8)dx
(\partial)/(\partial x)(y-ln(sqrt(xy)))	\frac{\partial\:}{\partial\:x}(y-\ln(\sqrt{xy}))
(d^2)/(dx^2)((14t^2+6)^{0.5})	\frac{d^{2}}{dx^{2}}((14t^{2}+6)^{0.5})
10x^{''}+1000x=0	10x^{\prime\:\prime\:}+1000x=0
derivative of (4pix^3/3)	\frac{d}{dx}(\frac{4πx^{3}}{3})
(e^x+e^{-x})^'	(e^{x}+e^{-x})^{\prime\:}
x(x+1)y^'+xy=1,y(e)=1	x(x+1)y^{\prime\:}+xy=1,y(e)=1
integral of (-(2xy)/((x^2+y^2)))	\int\:(-\frac{2xy}{(x^{2}+y^{2})})dy
(\partial)/(\partial x)((1+x)sin(y))	\frac{\partial\:}{\partial\:x}((1+x)\sin(y))
derivative of ln(axsqrt(a+x))	\frac{d}{dx}(\ln(ax\sqrt{a+x}))
integral of 1/((x^2-49)^{3/2)}	\int\:\frac{1}{(x^{2}-49)^{\frac{3}{2}}}dx
-y^'+(2y)/x =x^3y^2	-y^{\prime\:}+\frac{2y}{x}=x^{3}y^{2}
limit as t approaches 0 of 6/(1+t)	\lim\:_{t\to\:0}(\frac{6}{1+t})
derivative of f(x)=arcsin(x)	derivative\:f(x)=\arcsin(x)
integral of sqrt(1+(2x)^2)	\int\:\sqrt{1+(2x)^{2}}dx
y^{''}+2y^'+y=12e-t	y^{\prime\:\prime\:}+2y^{\prime\:}+y=12e-t
integral of csc^2(θ)-1	\int\:\csc^{2}(θ)-1dθ
integral of-e^{x^2}	\int\:-e^{x^{2}}dx
derivative of (4x-3^8)	\frac{d}{dx}((4x-3)^{8})
laplacetransform t^2+4	laplacetransform\:t^{2}+4
integral of x^{4/7}	\int\:x^{\frac{4}{7}}dx
integral of (sin(4x))	\int\:(\sin(4x))dx
limit as x approaches 4 of 1/(4-x)	\lim\:_{x\to\:4}(\frac{1}{4-x})
derivative of-sin(x^2*2x)	\frac{d}{dx}(-\sin(x^{2})\cdot\:2x)
y=(((x-3))/((x+2)))	y=(\frac{(x-3)}{(x+2)})
integral of (sec^2(3x))	\int\:(\sec^{2}(3x))dx
integral from 0 to r of sqrt((r^2-y^2))	\int\:_{0}^{r}\sqrt{(r^{2}-y^{2})}dy
integral of (8x^2)/((x^3+2)^3)	\int\:\frac{8x^{2}}{(x^{3}+2)^{3}}dx
integral of ((ln(x))^4)/x	\int\:\frac{(\ln(x))^{4}}{x}dx
integral from 1 to e of x^2ln(sqrt(x))	\int\:_{1}^{e}x^{2}\ln(\sqrt{x})dx
derivative of (y^4)/8+1/(4y^2)	derivative\:\frac{y^{4}}{8}+\frac{1}{4y^{2}}
5y^{''}+26y=0	5y^{\prime\:\prime\:}+26y=0
derivative of e^{x^2+9x+7}	derivative\:e^{x^{2}+9x+7}
sum from n=2 to infinity of 2nln(n)	\sum\:_{n=2}^{\infty\:}2n\ln(n)
integral of 9x^{2/3}	\int\:9x^{\frac{2}{3}}dx
limit as x approaches-infinity of 3-2^x	\lim\:_{x\to\:-\infty\:}(3-2^{x})
derivative of ln(x/(x^2+c))	derivative\:\ln(\frac{x}{x^{2}+c})
integral from 0 to 8 of 2/(x^{2/3)}	\int\:_{0}^{8}\frac{2}{x^{\frac{2}{3}}}dx
derivative of sqrt(5/x-1)	\frac{d}{dx}(\sqrt{\frac{5}{x}-1})
tangent of f(x)=x^4-13x^2+36,\at 1	tangent\:f(x)=x^{4}-13x^{2}+36,\at\:1
integral of (x^2-3x+2)/(x+1)	\int\:\frac{x^{2}-3x+2}{x+1}dx
integral of (5y^4)/(y^5-13)	\int\:\frac{5y^{4}}{y^{5}-13}dy
inverse oflaplace (50s)/(s^2+25)	inverselaplace\:\frac{50s}{s^{2}+25}
(\partial)/(\partial x)(e^{-x}y)	\frac{\partial\:}{\partial\:x}(e^{-x}y)
integral from-2 to 5 of \|-x^3+9x\|	\int\:_{-2}^{5}\left\|-x^{3}+9x\right\|dx
derivative of 4cot(x)	\frac{d}{dx}(4\cot(x))
derivative of f(x)=-5e^{-2.5x^2}x	derivative\:f(x)=-5e^{-2.5x^{2}}x
limit as x approaches 0 of x^3+2^2-x	\lim\:_{x\to\:0}(x^{3}+2^{2}-x)
xy(dy)/(dx)=1+y^2	xy\frac{dy}{dx}=1+y^{2}
y^'-2/x y=(y^5)/(x^2)	y^{\prime\:}-\frac{2}{x}y=\frac{y^{5}}{x^{2}}
derivative of (log_{e}(x)/(x^2))	\frac{d}{dx}(\frac{\log_{e}(x)}{x^{2}})
y^{''}-2y^'-3y=0	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=0
derivative of f(t)=sqrt(t)	derivative\:f(t)=\sqrt{t}
limit as x approaches 2 of x/(x+1)	\lim\:_{x\to\:2}(\frac{x}{x+1})
integral of (e^{-2x})/2	\int\:\frac{e^{-2x}}{2}dx
integral of 1/(2+5x^6)(30x^5)	\int\:\frac{1}{2+5x^{6}}(30x^{5})dx
integral of 1/(sqrt(25-x^2))	\int\:\frac{1}{\sqrt{25-x^{2}}}dx
tangent of f(x)=9x^2+6x-6	tangent\:f(x)=9x^{2}+6x-6
derivative of 7pix^2	derivative\:7πx^{2}
limit as x approaches 0+of 12e^{-2/x}	\lim\:_{x\to\:0+}(12e^{-\frac{2}{x}})
f(R)=R^3	f(R)=R^{3}
integral of (1+1/x)^{-3} 1/(x^2)	\int\:(1+\frac{1}{x})^{-3}\frac{1}{x^{2}}dx
integral of (y^2)/((y^2+3)^{3/2)}	\int\:\frac{y^{2}}{(y^{2}+3)^{\frac{3}{2}}}dy
limit as h approaches 0 of (sin(9h))/(9h)	\lim\:_{h\to\:0}(\frac{\sin(9h)}{9h})
limit as x approaches 0 of sqrt(x+9)-3	\lim\:_{x\to\:0}(\sqrt{x+9}-3)
derivative of (x^2/(x-8))	\frac{d}{dx}(\frac{x^{2}}{x-8})
integral of (x^2)/(x^2+x+6)	\int\:\frac{x^{2}}{x^{2}+x+6}dx
tangent of sqrt(x)+1/(sqrt(x^3))	tangent\:\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
limit as x approaches 2 of sqrt(x^2-4)	\lim\:_{x\to\:2}(\sqrt{x^{2}-4})
derivative of sin^2(5x^2)	\frac{d}{dx}(\sin^{2}(5x^{2}))

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