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Popular Calculus Problems

integral of 1/(1+cos^2(x))	\int\:\frac{1}{1+\cos^{2}(x)}dx
integral of 1/(u^2+u)	\int\:\frac{1}{u^{2}+u}du
inverse oflaplace ((s+2))/(s(s+4))	inverselaplace\:\frac{(s+2)}{s(s+4)}
derivative of tan(5x+5)	\frac{d}{dx}(\tan(5x+5))
integral from 0 to 3 of x/(sqrt(9-x^2))	\int\:_{0}^{3}\frac{x}{\sqrt{9-x^{2}}}dx
integral of 45sqrt(t)-(21)/(sqrt(t))	\int\:45\sqrt{t}-\frac{21}{\sqrt{t}}dt
derivative of 2/(x^3+1)	\frac{d}{dx}(\frac{2}{x^{3}+1})
derivative of (-5/(x^5))	\frac{d}{dx}(\frac{-5}{x^{5}})
integral of (x^2)/(csc(x))	\int\:\frac{x^{2}}{\csc(x)}dx
integral from 0 to 5 of 1/(x^{19/20)}	\int\:_{0}^{5}\frac{1}{x^{\frac{19}{20}}}dx
integral from 0 to 4 of (6-x^2)	\int\:_{0}^{4}(6-x^{2})dx
derivative of x^2-1/2 cos(x)	derivative\:x^{2}-\frac{1}{2}\cos(x)
derivative of f(x)=(x^4+3)(-4x^5+5x^4+5)	derivative\:f(x)=(x^{4}+3)(-4x^{5}+5x^{4}+5)
derivative of u	derivative\:u
derivative of 1/(sqrt(1+2x))	\frac{d}{dx}(\frac{1}{\sqrt{1+2x}})
integral of (x+4)ln(x)	\int\:(x+4)\ln(x)dx
sum from n=1 to infinity of 6(0.9)^{n-1}	\sum\:_{n=1}^{\infty\:}6(0.9)^{n-1}
integral of-4cos(x)-x	\int\:-4\cos(x)-xdx
derivative of (5x^3-3x+4^{20})	\frac{d}{dx}((5x^{3}-3x+4)^{20})
y^'=7y^5	y^{\prime\:}=7y^{5}
integral of x/(4+2x^2)	\int\:\frac{x}{4+2x^{2}}dx
derivative of c{f}(x+{f}(x)(cx))	\frac{d}{dx}(c{f}(x)+{f}(x)(cx))
derivative of 1/2 ln(x^2)	\frac{d}{dx}(\frac{1}{2}\ln(x^{2}))
integral of 1/(sin(x)-cos(x))	\int\:\frac{1}{\sin(x)-\cos(x)}dx
tangent of f(x)=2x(x^2-4x+5)^6,\at x=2	tangent\:f(x)=2x(x^{2}-4x+5)^{6},\at\:x=2
d/(dX)(X^2)	\frac{d}{dX}(X^{2})
integral from 1 to 3 of x^4(ln(x))^2	\int\:_{1}^{3}x^{4}(\ln(x))^{2}dx
derivative of 8e^{-2x}	derivative\:8e^{-2x}
f(x)=x-2sin(x)	f(x)=x-2\sin(x)
limit as x approaches 0 of 2/(x^6)	\lim\:_{x\to\:0}(\frac{2}{x^{6}})
sum from n=1 to infinity of (4^n)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{4^{n}}{n^{2}}
taylor 1/(sqrt(1+x^2))	taylor\:\frac{1}{\sqrt{1+x^{2}}}
derivative of f(x)=(x+2)/(x-2)	derivative\:f(x)=\frac{x+2}{x-2}
integral of ln((3x)^2)	\int\:\ln((3x)^{2})dx
integral of (-8x^2+16x+8)/((x-1)^2(x^2+1))	\int\:\frac{-8x^{2}+16x+8}{(x-1)^{2}(x^{2}+1)}dx
integral from 1 to 7 of sqrt(x-1)	\int\:_{1}^{7}\sqrt{x-1}dx
integral of (ln(ln(3x)))/(3x)	\int\:\frac{\ln(\ln(3x))}{3x}dx
limit as x approaches 3 of 5x^3-3x+x-6	\lim\:_{x\to\:3}(5x^{3}-3x+x-6)
(\partial)/(\partial x)(amx^bmy^{1-b})	\frac{\partial\:}{\partial\:x}(amx^{b}my^{1-b})
derivative of arccos(x^2)	\frac{d}{dx}(\arccos(x^{2}))
integral from 0 to 1 of (2x)/(e^{2x)}	\int\:_{0}^{1}\frac{2x}{e^{2x}}dx
tangent of y=2x^3+3x^2-12x+7	tangent\:y=2x^{3}+3x^{2}-12x+7
derivative of e^{2x}(2x+1)	\frac{d}{dx}(e^{2x}(2x+1))
limit as h approaches 0 of (sqrt(49+h)-7)/h	\lim\:_{h\to\:0}(\frac{\sqrt{49+h}-7}{h})
laplacetransform 2*sin(3t)	laplacetransform\:2\cdot\:\sin(3t)
area y=e^{3x},y=e^{-3x},x=-1	area\:y=e^{3x},y=e^{-3x},x=-1
integral from 0 to 2 of-6x^3sqrt(x^2+4)	\int\:_{0}^{2}-6x^{3}\sqrt{x^{2}+4}dx
derivative of 1+x+5x^2	\frac{d}{dx}(1+x+5x^{2})
integral from-2 to 1 of 2-x^2-x	\int\:_{-2}^{1}2-x^{2}-xdx
derivative of (x^9-1)^3	derivative\:(x^{9}-1)^{3}
derivative of (x^2-6x+1)/(x^2+7)	derivative\:\frac{x^{2}-6x+1}{x^{2}+7}
derivative of 1/2 e^{x/2}	\frac{d}{dx}(\frac{1}{2}e^{\frac{x}{2}})
y^{''}+4y^'=5	y^{\prime\:\prime\:}+4y^{\prime\:}=5
integral of 4/x+csc(x)cot(x)	\int\:\frac{4}{x}+\csc(x)\cot(x)dx
derivative of (4x/(1+x^2))	\frac{d}{dx}(\frac{4x}{1+x^{2}})
(dy)/(dx)= y/(x^2),y(1)=1	\frac{dy}{dx}=\frac{y}{x^{2}},y(1)=1
limit as x approaches 1+of 4/(x^{(1-x))}	\lim\:_{x\to\:1+}(\frac{4}{x^{(1-x)}})
derivative of sec^2(x-1)	\frac{d}{dx}(\sec^{2}(x)-1)
integral from 0 to pi/2 of 1/(x^2+2)	\int\:_{0}^{\frac{π}{2}}\frac{1}{x^{2}+2}dx
limit as x approaches infinity of (x^5)/(sqrt(x^{10)+9)}	\lim\:_{x\to\:\infty\:}(\frac{x^{5}}{\sqrt{x^{10}+9}})
derivative of f(x)=x^2sin(x)+2xcos(x)	derivative\:f(x)=x^{2}\sin(x)+2x\cos(x)
(dy)/(dx)=xy+2y	\frac{dy}{dx}=xy+2y
y^{''}-10y^'+25y=(4.5e^{5t})/(tt+1)	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=\frac{4.5e^{5t}}{tt+1}
(dy)/(dx)=6x^5cos^2(y)	\frac{dy}{dx}=6x^{5}\cos^{2}(y)
integral of (11x)/(x^4+1)	\int\:\frac{11x}{x^{4}+1}dx
integral of cot^3(x)(sec^2(x)-1)	\int\:\cot^{3}(x)(\sec^{2}(x)-1)dx
derivative of (100/x)	\frac{d}{dx}(\frac{100}{x})
limit as x approaches 0+of x^6ln(x)	\lim\:_{x\to\:0+}(x^{6}\ln(x))
y^'=(x^2)/(y^2)	y^{\prime\:}=\frac{x^{2}}{y^{2}}
integral from 1 to e of 4/x	\int\:_{1}^{e}\frac{4}{x}dx
derivative of x^3+1/x	\frac{d}{dx}(x^{3}+\frac{1}{x})
integral of 1/((2+x))	\int\:\frac{1}{(2+x)}dx
integral of (sin(2x))/(22+cos^2(x))	\int\:\frac{\sin(2x)}{22+\cos^{2}(x)}dx
derivative of e^x*sin(y)	\frac{d}{dx}(e^{x}\cdot\:\sin(y))
maclaurin x/((1+x^2)^2)	maclaurin\:\frac{x}{(1+x^{2})^{2}}
f(x)=2xe^{x^2}	f(x)=2xe^{x^{2}}
sum from n=0 to infinity}(1-10^{42 of)^n	\sum\:_{n=0}^{\infty\:}(1-10^{42})^{n}
derivative of ln(xsin(x))	\frac{d}{dx}(\ln(x)\sin(x))
(d^2y)/(dx^2)=3e^{-x},y(0)=1,y^'(0)=4	\frac{d^{2}y}{dx^{2}}=3e^{-x},y(0)=1,y^{\prime\:}(0)=4
integral of 1 1/(x^2)	\int\:1\frac{1}{x^{2}}dx
derivative of (((x+3))/(x-1))^2	derivative\:(\frac{(x+3)}{x-1})^{2}
y^'-2x=4x^3,y(0)=1	y^{\prime\:}-2x=4x^{3},y(0)=1
derivative of 7xln((16x)/(16x+1))	derivative\:7x\ln(\frac{16x}{16x+1})
(dy)/(dx)=2x+3y	\frac{dy}{dx}=2x+3y
integral of xe^{2x}	\int\:x\cdot\:e^{2\cdot\:x}dx
integral of 1/(3(x+1))	\int\:\frac{1}{3(x+1)}dx
integral of sqrt(x)cos(x)	\int\:\sqrt{x}\cos(x)dx
tangent of (8x)/(x^2+1),\at x=0	tangent\:\frac{8x}{x^{2}+1},\at\:x=0
integral from 0 to 3 of (xsqrt(14-x^2))	\int\:_{0}^{3}(x\sqrt{14-x^{2}})dx
(\partial)/(\partial θ)(ρsin(φ)sin(θ))	\frac{\partial\:}{\partial\:θ}(ρ\sin(φ)\sin(θ))
integral of (e^{2x})/(e^x+5)	\int\:\frac{e^{2x}}{e^{x}+5}dx
(\partial)/(\partial x)(y(-3-x))	\frac{\partial\:}{\partial\:x}(y(-3-x))
integral of cos(x)\sqrt[7]{5+sin(x)}	\int\:\cos(x)\sqrt[7]{5+\sin(x)}dx
(\partial)/(\partial x)(xy-x^2y)	\frac{\partial\:}{\partial\:x}(xy-x^{2}y)
(\partial)/(\partial x)(2xz^3e^{y^2})	\frac{\partial\:}{\partial\:x}(2xz^{3}e^{y^{2}})
integral of 1/(sqrt(1+z^2))	\int\:\frac{1}{\sqrt{1+z^{2}}}dz
derivative of f(x)=4(4e^x-25)^7	derivative\:f(x)=4(4e^{x}-25)^{7}
tangent of y=15-x^2,(1,14)	tangent\:y=15-x^{2},(1,14)
integral of x^5(2-5x^3)^{2/3}	\int\:x^{5}(2-5x^{3})^{\frac{2}{3}}dx
y^{''}+1=0	y^{\prime\:\prime\:}+1=0

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