# Class 12 Integration by parts

5115

Mathematics Integration Level: Misc Level

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

$\int x Sinx dx$

5116

Mathematics Integration Level: Misc Level

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

$\int xSin3xdx$

5117

Mathematics Integration Level: Misc Level

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

$\int xCos2xdx$

5118

Mathematics Integration Level: Misc Level

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

$\int \left ( e^{logx}+Sinx \right )Cosxdx$

5122

Mathematics Integration Level: Misc Level

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

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

5123

Mathematics Integration Level: Misc Level

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

$\int e^{2x}Sinxdx=I$

5124

Mathematics Integration Level: Misc Level

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

$\int \frac{xCos^{-1}x}{\sqrt{1+x^{2}}} dx$

5125

Mathematics Integration Level: Misc Level

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

$\int tan^{-1}\big( \frac{3x-x^{3}}{1+3x^{2}}\big) dx=I$

5126

Mathematics Integration Level: Misc Level

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

$\int Cos\sqrt{x}dx$

5127

Mathematics Integration Level: Misc Level

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

$\int x^{3}tan^{-1}(x^{2})dx=\int x^{2}tan^{-1}xdx$

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