5174

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0  or  \int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x2

(ii) For x2 + A in the numerator put x - A/x =t as substitution . And for x2 - A in the numerator, put x + A/x = t

\int \frac{1-x^{2}}{1+x^{4}}dx



5163

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute x^{2}=y to make partial fractions. Once the partial fractions are formed substitute back y=x^{2} and integrate.

\int \frac{Sinx}{Sin4x}dx



5162

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute x^{2}=y to make partial fractions. Once the partial fractions are formed substitute back y=x^{2} and integrate.

\int \frac{x^{2}}{1-x^{4}}dx



5161

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute x^{2}=y to make partial fractions. Once the partial fractions are formed substitute back y=x^{2} and integrate.

\int \frac{x^{2}}{x^{4}-x^{2}-12}dx=I



5160

Mathematics Integration Level: Misc Level

Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute x^{2}=y to make partial fractions. Once the partial fractions are formed substitute back y=x^{2} and integrate.

\int \frac{x^{2}}{(x^{2}+1)(x^{2}+4)}dx=I

 



5159

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int \frac{Sin^{-1}x}{x^{2}}dx



5158

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int Cosec^{3}xdx=I



5157

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int e^{x}Sin^{2}xdx



5156

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int e^{ax}Cos(bx+c)dx



5136

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int x^{2}log(1+x)dx



5135

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int logxdx



5134

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int xlog2xdx



5133

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int x^{2}Sin^{-1}xdx



5132

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int Cos^{-1}\big( \frac{1}{x} \big)dx



5131

Mathematics Integration Level: Misc Level

Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential

\int x^{3}Sin(x^{2})dx

Displaying 166-180 of 195 results.

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